The ventral tegmental area (VTA), which is located in the midbrain, is a major sources of dopamine neurons in the brain, and is involved in a variety of brain functions (Morales and Margolis, 2017). Specifically, dopamine neurons in the VTA are best characterized as a key regulator of reward- and stress-associated behaviors (Russo and Nestler, 2013; Fox and Lobo, 2019). The VTA receives inputs from many brain regions (Zahm et al., 2011; Watabe-Uchida et al., 2012; Beier et al., 2015), and the DCN was shown to be a region projecting to the VTA (Snider et al., 1976; Parker et al., 2014; Beier et al., 2015; Carta et al., 2019). Presumably owing to the relatively minor connections, cerebellar projections to the VTA were not always detected (Teune et al., 2000). Nevertheless, sophisticated viral-genetic tracing of the input-output organization of the VTA clearly demonstrated the monosynaptic connection from the DCN to the VTA (Beier et al., 2015). Functional excitatory synaptic connections from the DCN neurons were also confirmed in not only dopamine neurons, but also GABAergic neurons in the VTA, using optogenetic stimulation of DCN neurons (Carta et al., 2019). Thus, even though anatomical connections from the DCN to the VTA appear to be minor, the VTA receives direct inputs from the DCN. It was originally suggested that projections originate from the FN and DN (Parker et al., 2014), yet a study in preprint at this moment showed using adeno-associated virus (AAV)-based circuit mapping that the DCN-VTA connections were contralateral, and originated mainly from the DN and partly from the IPN (Baek et al., 2021). The study also showed that among all the VTA regions, the dorsolateral posterior VTA was the main target of the DCN projections.

Consistent with the functional connections from the DCN to the VTA, activation of this pathway was shown to contribute to reward- and stress-associated behaviors (Figure 1B). Using optogenetic manipulation of axons of DCN neurons in the VTA, activation of this pathway was demonstrated to be rewarding and to be required for social behaviors (Carta et al., 2019). On the other hand, it was demonstrated in the abovementioned preprint study using chemogenetic manipulation of VTA-projecting DCN neurons that chronic activation of these neurons triggers depression-like behaviors (Baek et al., 2021). Although it is still unknown as to how the activation of the DCN efferent pathways projecting to the VTA can positively and negatively affect mental conditions, i.e., rewarding and depression, this may be reasonable given the heterogeneous functions of the VTA (Morales and Margolis, 2017).

Where the VTA neurons receiving inputs from the cerebellum project to is an important question. It was shown that cerebellar activation triggers dopamine release in the medial prefrontal cortex (mPFC) (Rogers et al., 2011, 2013), suggesting that the cerebellum affects emotional states via the regulation of dopamine release in the mPFC. It would be interesting to further analyze these cerebellum-VTA neuronal circuits by additional anatomical studies using transsynaptic tracing and by physiological studies measuring dopamine release and neuronal activity.

The periaqueductal gray (PAG) in the midbrain takes the form of a longitudinal column (Bandler and Shipley, 1994), and receives many types of neuronal inputs (Tovote et al., 2015; George et al., 2019). The PAG is known to be associated with active and passive responses to threat (Gross and Canteras, 2012; Tovote et al., 2015; George et al., 2019), including freezing behavior, which has often been used to measure fear responses in rodent (Roelofs, 2017). Both learned and innate freezing behaviors are mediated by the activity of glutamatergic neurons in the ventrolateral PAG (vlPAG) that project to the magnocellular nucleus, and their activity is regulated by different types of inputs, such as GABAergic inputs from the amygdala and glutamatergic inputs from the prefrontal cortex (Tovote et al., 2016; Rozeske et al., 2018). The vlPAG includes not only glutamatergic neurons, but also diverse populations of neurons, including GABAergic, serotonergic, and dopaminergic neurons (Suckow et al., 2013; Taylor et al., 2019).

Anterograde tracing studies demonstrated that DCN neurons, mainly in the FN and DN, send axonal projections to the PAG (Gonzalo-Ruiz and Leichnetz, 1990; Teune et al., 2000), and direct projections from the FN to the vlPAG were further confirmed by recent studies using AAV- or retrograde tracing-based mapping (Frontera et al., 2020; Vaaga et al., 2020). DCN neurons in the FN make synapses onto diverse types of neurons in the vlPAG, because studies have demonstrated anatomical and functional synaptic connections onto glutamatergic, GABAergic, and dopaminergic neurons of the vlPAG (Frontera et al., 2020; Vaaga et al., 2020). Considering the possible involvement of the cerebellum in freezing behaviors (Supple et al., 1987, 1988; Sacchetti et al., 2002, 2004; Koutsikou et al., 2014), the identification of network connections would lead to the idea that the cerebellar regulation of vlPAG plays a role in freezing behaviors. One study supported this idea by showing that cerebellar inputs from the FN modulate dopamine interneurons in the vlPAG and in turn regulate the activity of Chx10-expressing glutamatergic neurons in the vlPAG, which reliably triggered freezing upon activation (Vaaga et al., 2020). Another study using direct chemogenetic manipulation of the FN-vlPAG pathway further demonstrated that this pathway bidirectionally regulates the strength of the fear memory formed during conditioning: increased activity weakened the memory, and decreased activity strengthened the memory (Frontera et al., 2020). As altered synaptic regulation in the cerebellum led to the enhancement of fear memory, and such cerebellum-mediated fear memory correlated with the increase in activity of the fear circuitry, in regions such as the amygdala and prefrontal cortex (Han et al., 2021), the FN-vlPAG pathway may not only regulate freezing behaviors as a fear response, but also fine tune the formation of fear memory through affecting fear circuitry (Figure 1B).

The dorsal raphe nucleus (DRN) is located in the midbrain and the pons, and is implicated in many functions through its projections to broad areas (Walker and Tadi, 2021). The DRN is composed of a heterogeneous population of neurons, in terms of the types of neurotransmitters, their molecular expression, and projection patterns (Huang et al., 2019; Ren et al., 2019). It is well known that the DRN is a major source of serotonin neurons, yet other neurotransmitters also play important roles in DRN functions (Liu et al., 2014; Li et al., 2016; Lin et al., 2020). One important function of the DRN is reward processing (Luo et al., 2015). Serotonergic neurons in the DRN have also been shown to have antidepressive effects (Urban et al., 2016; You et al., 2016; Nishitani et al., 2019), which are presumably linked to reward processing. The heterogeneity of the DRN also arises from the complex and diverse inputs from many brain regions, one of which is the DN (Pollak Dorocic et al., 2014; Ren et al., 2018). Although the role of the DN-DRN pathway has not been clarified, it may cooperate with the DN-VTA pathway to regulate reward- and stress-associated behaviors. Mapping studies of inputs to the DRN (Pollak Dorocic et al., 2014; Ren et al., 2018) demonstrated that the DRN receives direct inputs from the DN, but not from the FN that is innervated by PCs in the cerebellar vermis. On the other hand, electrical stimulation of the vermis of depressed animals led to their recovery from depressive symptoms and an increase in firing of DRN serotonergic neurons (Bambico et al., 2018). Considering these studies, there may be an indirect pathway from the vermis and FN to the DRN that causes antidepressive effects (Figure 1B), in addition to the direct pathway from the DN to the DRN.

In concurrence with dopamine and serotonin, noradrenaline is also an important neuromodulator that affects mental conditions (Ruhé et al., 2007; Nutt, 2008). The locus coeruleus (LC), which is located in the brainstem just under the cerebellum, is a major noradrenergic source in the brain. The LC-noradrenaline system is involved in a wide range of behaviors, such as arousal, attention, motivation, and stress responses (Benarroch, 2009; Eschenko et al., 2017; Poe et al., 2020; Ross and Van Bockstaele, 2020), although the dopamine release from LC neurons has also been shown to have various functions (Kempadoo et al., 2016; Takeuchi et al., 2016; Beas et al., 2018). Like other brain regions discussed in this section, the LC also receives inputs from and sends outputs to a wide variety of brain regions. Interestingly, not only DCN neurons, but also cerebellar PCs directly send axonal projections to the LC (Schwarz et al., 2015; Breton-Provencher and Sur, 2019). As the vestibular nucleus, which is another structure receiving direct inputs from PCs, is also located in the brainstem just under the cerebellum, direct PC projections might be a common feature among these brainstem regions. The LC-projecting PCs are distributed throughout the ipsilateral cerebellar vermis (Schwarz et al., 2015), and innervate both GABAergic and noradrenergic neurons in the LC (Breton-Provencher and Sur, 2019). It would be interesting to establish a technique to specifically manipulate LC-projecting PCs or LC neurons regulated by PCs, and to investigate their specific functions.

In addition to the abovementioned brain regions, DCN neurons directly project to a wide variety of other brain regions, such as parafascicular thalamic nucleus, zona incerta, substantia nigra (SN), parabrachial nucleus, laterodorsal tegmental nucleus, pedunculopontine tegmental nucleus, nucleus incertus, and supramammillary region (Teune et al., 2000; Fujita et al., 2020; Kebschull et al., 2020). Although some of them will be described in the next section regarding indirect pathways, we don’t discuss many of them in this article, because their precise functions and network properties have not yet been identified. Nevertheless, we hope that these pathways will be studied in the near future. Specifically, the direct projections to the SN and the zona incerta from the DN (Teune et al., 2000; Watabe-Uchida et al., 2012; Kebschull et al., 2020) might be worth investigation, given their close association with the basal ganglia, which is another brain region responsible primarily for motor control, and is also associated with non-motor functions. As the cerebellum and the basal ganglia have indirect network connections, and their functional interactions have often been described, we will discuss them in the next section. The cerebellum is generally considered to operate prediction of motor and non-motor events (Sokolov et al., 2017; Hull, 2020) by integrating efferent copy and sensory feedback. The signals to fine-tune specific functions are likely then delivered through designated efferent projections to other brain regions responsible for the functions. Thus, projections to a broad range of brain regions may be crucial for cerebellar multifunctionality.

The mPFC is implicated in various cognitive functions, such as emotional control, motivation, fear extinction, sociability, decision making, and long-term and short-term memory (Euston et al., 2012; Grossmann, 2013; Peters et al., 2013; Domenech and Koechlin, 2015; Giustino and Maren, 2015; Xu et al., 2019). Given such a wide range of cognitive functions, an idea was proposed that the general role of the mPFC is to resolve conflicting responses (Euston et al., 2012; Peters et al., 2013), presumably by taking into account positive and negative information carried by broad types of inputs, and providing contextually appropriate neuronal signals. The interaction between the cerebellum and the mPFC has been reported in several studies, including studies recording synchronized oscillations in rodents and functional connectomics analyses in humans or primates (Ramnani, 2006; Kalmbach et al., 2009; Chen et al., 2016; Stoodley et al., 2017; McAfee et al., 2019), the latter of which suggested connections in the direction from the cerebellum to the mPFC. Experiments in rodents showed that electrical stimulation of the FN evoked local-field potentials in the mPFC (Watson et al., 2014), implying that cerebellar outputs functionally connect to the mPFC. Anatomical connections from the DN to the mPFC through the thalamus were also demonstrated in primates using retrograde transneuronal transport of herpes simplex virus type 1 (Middleton and Strick, 2001). Based on these studies, it has become clear that cerebellar neurons indirectly project to the mPFC through the thalamus, in addition to oppositely directed connections from the mPFC to the cerebellum through the pontine nucleus (Kalmbach et al., 2009). A recent study demonstrated functions of the cerebellar-mPFC pathway on behaviors associated with autism spectrum disorders (ASDs) (Kelly et al., 2020). Specifically, two cerebellar efferent pathways to the mPFC were found to be responsible for the various phenotypes observed in cerebellar dysfunction-dependent ASDs: a pathway from crus I in the cerebellar cortex to the DN, and another pathway from the cerebellar posterior vermis to the FN, converging on the ventromedial thalamus projecting to the mPFC, which were involved in the regulation of social performance and behavioral flexibility, respectively.

The cerebellum-dependent regulation of mPFC may be in part through dopamine release, because the electrical stimulation of lobule IV/V PCs and the DN were shown to evoke dopamine release in the mPFC (Mittleman et al., 2008). Two possibilities were discussed in this previous paper regarding pathways from the DCN that regulate dopamine release in the mPFC. The first is the pathway from the DN or IPN to the VTA through the reticulotegmental nuclei in the pons, and to the pedunculopontine tegmental nuclei. The second is the pathway from the DCN to the mediodorsal and ventrolateral thalamic nuclei, via which glutamate neurons control dopamine release by regulating presynaptic terminals in the mPFC. As DCN neurons directly project to the VTA (Snider et al., 1976; Parker et al., 2014; Beier et al., 2015; Carta et al., 2019; Baek et al., 2021), this direct projection may in turn regulate dopamine release in the mPFC. All pathways shown or suggested to date may mediate cerebellar-mPFC circuits (Figure 1C), and regulation through these various pathways appears to be reasonable, considering the functions of the mPFC, which require broad types of inputs.

The motor cortex can be divided into the primary and premotor areas. The primary motor cortex, which is a well-known region that receives connections from the cerebellum through the thalamus, is thought to have a predominant role in motor execution. The anterolateral motor cortex (ALM) in mice is thought to be equivalent to the premotor cortex in primates, and to be involved in motor planning by presenting preparatory activity that is crucial for subsequent proper movements (Guo et al., 2014; Li et al., 2015). In addition to the primary motor cortex, functions of cerebellar projections to the ALM have recently been identified, in an effort to understand cerebellar cognitive functions. Studies have shown that optogenetic excitation of the DCN alters preparatory activity in the ALM, indicating the importance of cerebellar-ALM pathways in motor planning (Gao et al., 2018; Chabrol et al., 2019). However, two studies showed different pathways working in motor planning, either from the FN or from the DN to the ALM (Figure 1C). Axons of DCN neurons from the FN and the DN were mainly present in the ventral medial nucleus and the ventral anterior-lateral nucleus of the thalamus, respectively. Both nuclei overlapped with thalamic regions that projected to the ALM, although overlapping regions of axons from the FN were much wider than those of axons from the DN (Gao et al., 2018). As suggested in a previous study (Chabrol et al., 2019), further analysis is required to solve questions as to whether these efferent projections work separately on motor planning in different behavioral paradigms, or actually cooperate with each other.

The connections between the cerebellum and the cerebral cortex are often bidirectional, involving the cortico-cerebellar pathway through the pontine nucleus and the cerebello-cortical pathway through the thalamus (Kelly and Strick, 2003; Krienen and Buckner, 2009; Buckner et al., 2011; Proville et al., 2014; Léna and Popa, 2016; Palesi et al., 2017; Brissenden et al., 2018; Gao et al., 2018). Intriguingly, not only bidirectional connections, but also closed-loop circuits are formed, which are composed of networks of the cerebellar regions projecting to the cerebral cortical regions that then project back to the same cerebellar regions (Proville et al., 2014; Gao et al., 2018). These closed-loop circuits may be effective for the precise adjustment or amplification of neuronal signals, and indeed, the sensorimotor cortico-cerebellar loop and the premotor cortico-cerebellar loop were shown to be important for fine movement control and for persistent preparatory activity, respectively (Proville et al., 2014; Gao et al., 2018).

The basal ganglia are a group of subcortical nuclei, which generally include the striatum consisting of the caudate and putamen, the internal (GPi) and external (GPe) segments of globus pallidus, the substantia nigra pars reticulata (SNr) and pars compacta (SNc), and the subthalamic nucleus (STN) (Lanciego et al., 2012; Purves et al., 2018). The basal ganglia can be broadly categorized into three nuclei, namely, the input nucleus of the striatum, the intrinsic nuclei of the GPe, SNc, and STN, and the output nuclei of the GPi and SNr. As with the cerebellum, the basal ganglia have also been implicated in motor control. Although both the cerebellum and basal ganglia have connections with the motor cortex, they are traditionally thought to have distinct roles in movement, with the cerebellum involved in real-time fine tuning of movement, and the basal ganglia involved in the production of action command (Doya, 2000), by projecting to different thalamic nuclei. This view has gradually been revised, mainly from three aspects. First, outputs from the cerebellum and the basal ganglia are not completely segregated, but interact with each other in the thalamus (Bosch-Bouju et al., 2013; Hintzen et al., 2018). Second, roles of both the cerebellum and the basal ganglia are not limited to motor control, but extend to cognitive functions (Doya, 2000; Middleton and Strick, 2000; Bostan and Strick, 2018; Pierce and Péron, 2020). Third, whereas interactions between the cerebellum and the basal ganglia are generally considered to be through the cerebral cortex, their reciprocal connections that do not include the cerebral cortex have also been identified (Bostan and Strick, 2018). In particular, there may be several pathways in the direction from the cerebellum to the basal ganglia (Figure 1D, next paragraph).

The disynaptic anatomical connections from the cerebellum to the basal ganglia were first demonstrated in rodents by observation of the overlap and synaptic contacts in the central lateral nucleus of the thalamus, between anterogradely labeled DN neuron axons and retrogradely labeled neurons projecting to the striatum (Ichinohe et al., 2000). Similar connections were then confirmed in primates by the transneuronal transport of rabies virus (Hoshi et al., 2005). Considering the time required for transneuronal transport, cerebellar outputs, partially from the IPN and FN, but mostly from the DN, disynaptically project to the putamen in the striatum presumably through the thalamus, including the central lateral nucleus. The connections from the DN to the striatum through the intralaminar thalamic nuclei, including the central lateral nucleus, were also functionally confirmed in rodents (Chen et al., 2014). In this previous study, a short latency of activity modulation was detected in the striatum upon the electrical or optogenetic stimulation of the DN, and the modulation was no longer detected when the intralaminar thalamus was inhibited. Importantly, the cerebello-striatal network through the thalamus was shown to be involved in the cognitive flexibility observed in mice performing a striatum-dependent reward-driven task (Xiao et al., 2018).

In addition to the connections from the DCN to the striatum through the intralaminar thalamus, other pathways are also likely to contribute to the functional interaction between the cerebellum and the basal ganglia. A possibility was recently proposed that the DCN makes disynaptic connections with the STN through the parafascicular nucleus of the thalamus (Watson et al., 2021). Because the nucleus accumbens (NAc) has sometimes been considered as a part of the basal ganglia based on its projections to the GPe and SN (Salgado and Kaplitt, 2015), one of the cerebellar-basal ganglia pathways may be from the DCN to the NAc through the VTA, of which projection to the NAc has been well characterized (Russo and Nestler, 2013). Although its functions are not yet determined, the direct connections from the DCN to the SN (Teune et al., 2000; Watabe-Uchida et al., 2012) may be involved in the cerebellar regulation of the basal ganglia. Considering that the SN can be categorized as an output nucleus of the basal ganglia, and that, as described here, there are several possible pathways from the cerebellum to the basal ganglia, the cerebellum may regulate the basal ganglia in a variety of ways (Figure 1D). It has been suggested that the cerebellum is involved in both pathophysiological and compensatory mechanisms of Parkinson’s disease (Martinu and Monchi, 2013), and such bidirectional involvement might be reasonable, considering that there are many pathways, through which the cerebellum regulates the basal ganglia.

The hippocampus is one of the most studied regions of the brain, and is well known to be crucial for learning, memory, and spatial navigation (Eichenbaum, 2004; Bird and Burgess, 2008). Even though connections from the cerebellum to the hippocampus were suggested a long time ago by electrophysiological recordings from the hippocampus upon cerebellar stimulation, and by observation of degenerating axons in the hippocampus after damage to the FN (Heath and Harper, 1974; Snider and Maiti, 1976; Heath et al., 1978; Newman and Reza, 1979), anatomical connections have only recently been reported. Studies using viral vector-based circuit tracing showed disynaptic and trisynaptic connections from the cerebellum to the hippocampus (Bohne et al., 2019; Watson et al., 2019), and specifically, tracing using a retrograde transneuronal property of rabies virus suggested several pathways (Figure 1E). Although the precise pathways between the DCN and the dentate gyrus in the hippocampus still need to be identified, vermal lobule VI and crus I of the cerebellar cortex appear to be regions that affect the hippocampus through the FN and the DN, respectively (Watson et al., 2019). Functional implications of cerebellar-hippocampal circuit connections have also been analyzed recently. Alterations of cerebellar activity were detected during hippocampus-dependent tasks (Iglói et al., 2015; Yu and Krook-Magnuson, 2015; Babayan et al., 2017). Cerebellar-specific gene manipulation and optogenetic excitation affected hippocampus-dependent behaviors (Rochefort et al., 2013; Lefort et al., 2019; Zeidler et al., 2020). It would be interesting to identify the precise cerebellar-hippocampal pathway, as this would enable us to specifically manipulate the pathway and subsequently identify its specific functions.

Amygdala is well known to play a role in the expression of fear and in the processing of fear-associated signals (Ehrlich et al., 2009; Ressler, 2010). As described in the section on direct efferent pathways, accumulating lines of evidence indicate the involvement of the cerebellum in the presentation of fear responses and the formation of fear memory (Sacchetti et al., 2002, 2004; Moreno-Rius, 2018; Ernst et al., 2019; Vaaga et al., 2020; Han et al., 2021). Consistent with the functional relevance, connections between the cerebellum and the amygdala were suggested in functional magnetic resonance imaging studies in human subjects (Dean et al., 2014; Nicholson et al., 2015; Leutgeb et al., 2016). Connections from the cerebellum to the amygdala were also demonstrated in rodents by functional analyses. Activation of the FN or anterior IPN resulted in the inhibition of central amygdala activity (Magal and Mintz, 2014), and the cerebellum-mediated enhancement of fear memory was shown to correlate with the activity increase in the amygdala (Han et al., 2021). Anatomical pathways were then suggested, in which the cerebellar FN could project to the basolateral amygdala through the parafascicular thalamus (Figure 1E; Frontera et al., 2020). Alternatively, because the parabrachial nucleus receives projections directly from PCs and indirectly through the FN (Hashimoto et al., 2018), and projects to the amygdala (Saper and Loewy, 1980; Jhamandas et al., 1996; Cai et al., 2018), the efferent pathways to the amygdala might be mediated via the parabrachial nucleus. Considering the potential of motor training as a therapy for abnormal fear responses (Faria et al., 2018; Tanner et al., 2018), the cerebellar-amygdala pathways may be worthy of further investigation.

In early studies, cerebellar efferent projections were tested using the Fink-Heimer method (Fink and Heimer, 1967) in animals with lesions in the DCN (Snider et al., 1976; Faull and Carman, 1978; Tang et al., 1987), in which degenerated nerve terminals of DCN neurons could be observed in target regions. Autoradiography was also used after DCN injection with radiolabeled amino acids that can be taken up by neurons (Angaut et al., 1985a,b). Although there may have been potential concerns about the observation being under unphysiological or toxic conditions, these studies suggested the importance of performing further research regarding cerebellar network connections. Horseradish peroxidase (HRP) was used as a less toxic retrograde tracer (Roldán and Reinoso-Suárez, 1981; Kawamura et al., 1982), although the efficiency of neuronal uptake was relatively low (Saleeba et al., 2019). In recent years, anterograde and retrograde tracers have been developed, improved, and frequently used owing to their convenience: tracers without serious safety concerns are commercially available and have sufficiently strong signals. The injection of anterograde tracers into the DCN increased our understanding of the overall projection patterns from the DCN (Teune et al., 2000). On the other hand, the injection of retrograde tracers into a target region resulted in the labeling of a specific group of DCN neurons (Lu et al., 2013; Houck and Person, 2015; Frontera et al., 2020; Vaaga et al., 2020). Even though tracers are convenient tools, we also need to understand their drawbacks (Saleeba et al., 2019). One point to consider is that the specificity of labeling basically relies on their localized injection.

Viral vector-based labeling has become a basic method for studies on the anatomical properties of neuronal circuits (Sarno and Robison, 2018; Haggerty et al., 2020; Liu et al., 2020; Xu et al., 2020). Unlike chemical tracers, viral vectors generally enable cell type- or network-specific labeling, by combining multiple viral injections or the use of transgenic mice with the expression of Cre recombinase (Cre). Given the heterogeneous properties of DCN neurons, investigations using specific labeling provide an accurate understanding of cerebellar efferent networks. Indeed, network property analyses in a cell type-specific manner were performed by injecting AAV with a Cre-dependent cassette into the DCN of cell type-specific Cre transgenic mice (Lefler et al., 2014; Ankri et al., 2015; Prekop et al., 2018; Zhou M. et al., 2020). Some studies also used viral vectors demonstrating retrograde transport, such as AAVs engineered to have efficient retrograde access [rAAV2-retro, (Tervo et al., 2016)] or a canine adenoviral vector [CAV2 (Del Rio et al., 2019)], to label projection-specific DCN neurons (Hashimoto et al., 2018; Frontera et al., 2020; Sathyamurthy et al., 2020; Baek et al., 2021). To observe disynaptic connections from the DCN, anterograde transsynaptic tracing was also performed (Xiao et al., 2018; Bohne et al., 2019; Kelly et al., 2020) by injecting recombinase-expressing AAV serotype 1 with transsynaptic properties (Zingg et al., 2017) or AAV expressing Cre fused with wheat germ agglutinin (WGA) (Gradinaru et al., 2010) into the DCN (Xiao et al., 2018; Bohne et al., 2019; Kelly et al., 2020). In these experiments, Cre- or flippase-dependent molecular expression was usually triggered by AAV injection into the intermediate region or by usage of reporter mice. Moreover, polysynaptic connections from the cerebellum were analyzed using the retrograde and anterograde transneuronal viral tracers, rabies virus (RV) and herpes simplex virus strain H129, respectively, which enabled dissection of the complex connections from the cerebellum to the hippocampus or the neocortex (Watson et al., 2019; Pisano et al., 2021).

Advanced anatomical analyses have the potential to increase our understanding of cerebellar efferent neuronal circuits. Systematic analyses of single-cell gene expression and anatomical projection mapping have characterized heterogeneous DCN neurons (Fujita et al., 2020; Kebschull et al., 2020). The results of these studies indicate that DCN neurons are subdivided into finer groups than expected, and individual groups at least in part have their own functions through their projections. These results share common traits with the traditional idea that the three nuclei of the DCN have different functions, yet greatly advanced our understanding of the cerebellar efferent pathways from the DCN. A tracing technique using a combination of a viral-genetic tool, named TRIO, was developed to analyze input and output organizations, and this sophisticated analysis confirmed previously unappreciated cerebellar projections into the neuromodulatory system, and further demonstrated the region of projection through the disynaptic pathways (Beier et al., 2015; Schwarz et al., 2015; Ren et al., 2018).

In addition to anatomical investigations, neuronal network connections between the cerebellum and other brain regions have been functionally tested by several techniques, including viral vector-based expression of optogenetic molecules. The most direct measurement method of functional connections is electrophysiological recording from target regions during electrical, optogenetic, or chemogenetic manipulation of cerebellar activity (Krook-Magnuson et al., 2014; Proville et al., 2014; Bambico et al., 2018; Gao et al., 2018; Carta et al., 2019; Chabrol et al., 2019; Frontera et al., 2020; Kelly et al., 2020; Zeidler et al., 2020; Dacre et al., 2021). The immunohistochemical analysis of activity-dependent molecules in target regions can be also used to detect activity changes in these regions after cerebellar manipulation (Xiao et al., 2018; Zeidler et al., 2020; Pisano et al., 2021). Alterations of molecular expression patterns specifically in the cerebellum may disrupt the functional integrity of the cerebellum, and in turn result in activity changes in other brain regions (Kelly et al., 2020; Rudolph et al., 2020; Han et al., 2021). Activity changes in these studies denote that the cerebellum has functional effects on the recorded brain regions through direct or indirect network connections. The direct functional connections have been verified by recording synaptic transmission from the neurons in target brain regions ex vivo, upon the photostimulation of channelrhodopsin-expressing DCN neuronal terminals (Gornati et al., 2018; Xiao et al., 2018; Carta et al., 2019; Vaaga et al., 2020; Baek et al., 2021).

Optogenetic and chemogenetic tools are beneficial to understand the roles of specific neuronal circuits in many types of brain functions and dysfunctions [e.g. (Muir et al., 2019; Biselli et al., 2021)]. Studies on the functions of cerebellar efferent pathways on a behavioral level have also benefited from these tools. In particular, optogenetic molecules were expressed in DCN neurons by the injection of AAV into the DCN, and photostimulation was applied to the target brain regions, which enabled the manipulation of specific cerebellar efferent pathways during behavioral analyses, and thus leading to an understanding of their functions (Carta et al., 2019; Kim et al., 2020; Dacre et al., 2021). The manipulation of specific cerebellar efferent pathways can also be achieved by specific molecular expression using a combination of viral vector injections. In these experiments, the abovementioned rAAV-retro or CAV2 expressing Cre was injected into target brain regions, and AAVs triggering Cre-dependent expression of chemogenetic or optogenetic molecules were injected into the DCN, which resulted in the specific expression of molecules in the DCN neurons projecting to the target brain regions. The manipulation of these neurons during behavioral tests by chemogenetic drug administration or photostimulation of the DCN clarified the functions of these efferent pathways (Frontera et al., 2020; Sathyamurthy et al., 2020; Baek et al., 2021; Wagner et al., 2021). Furthermore, disynaptically connected cerebellar efferent pathways were also investigated, as follows: AAV serotype 1 expressing Cre, or AAV expressing WGA-Cre was injected into the DCN, and AAV triggering the Cre-dependent expression of chemogenetic or optogenetic molecules was injected into the intermediate regions, which resulted in the expression of these molecules specifically in neurons of the intermediate regions receiving inputs from the DCN. The functions of disynaptic efferent pathways were then tested by specifically applying a chemogenetic drug or by photostimulation to the target brain regions during the behavioral analyses (Xiao et al., 2018; Kelly et al., 2020).