This thesis includes two directions of research regarding the function and physiology of the cerebellum. One direction was concentrated on the cerebellum involvement in motor control during a visually guided tracking task performed by non-human primates. The second effort aimed to characterize the effects of the P/Q-type Ca2+ channelopathy on the physiology of the cerebellar cortex in tottering mice and to explore the mechanisms that transform homeostatic deficits due to genetic mutations into transient phenotype such as episodic dystonia. Understanding the cerebellum function is an ongoing challenge. The cerebellum has been implicated in error processing required for on-line motor control and motor learning. The dominant view is that the error related signals are encoded by the Purkinje cell complex spike discharge. The results presented in this thesis show that the Purkinje cell simple spike activity robustly signals a rich representation of task specific performance errors, independently from the kinematic signals. The results also show that a large majority of the Purkinje cells encode behavioral parameters dually by a pair of signals, one predictive and one feedback related. The predictive signals could provide the neural substrate for the feedback-independent compensatory movements that maintain motor behavior accuracy. The dual representation is also consistent with the signals needed to generate the prediction sensory error used to update an internal model. These results provide new insights into the cerebellum function and have interesting implications for the forward internal model hypothesis. The tottering mouse is an autosomal recessive disorder involving a mutation in the gene encoding the P/Q-type Ca2+ channels and is one of the animal models for the episodic ataxia type 2. The most remarkable aspect of the tottering mouse phenotype are the transient attacks of dystonia triggered by stress, ethanol or caffeine. The neural processes underlying the transient phenotype are unknown. The results presented in this thesis, based on the flavoprotein autofluorescenece imaging, show that the tottering mouse dysfunction is associated with the presence of transient synchronous low frequency oscillations in the cerebellar cortex. For a large majority of cerebellar cortical neurons the optical oscillations reflect the oscillations present in their spontaneous activity. The oscillations appear to be intrinsic to the cerebellar cortex and in the awake animals increased oscillatory cerebellar activation becomes highly coherent with the EMG activity during episodic dystonia. Low frequency oscillations of the cerebellum represent a novel abnormality in the tottering mouse and could provide insights into the mechanism underlying the transient phenotype of the episodic ataxia type 2.