The cerebellum is a major motor control structure with a highly ordered circuity. The parallel fibers (PFs) are a dominant element of the cerebellar circuitry. Parallel fibers are the bifurcated axons of the granule cells (GCs) that project across the surface of the cerebellar cortex and synapse on the major output neuron, the Purkinje cell (PC). However, the role of PFs in the cerebellum has long been controversial and a matter of intense debate. Early studies inspired the "beam" hypothesis whereby GC activation results in PF driven, post-synaptic excitation of beams of PCs. However, the "radial" hypothesis postulates that the ascending limb of the GC axon provides the dominant input to PCs and generates patch-like PC responses. To address the beam versus patch controversy and PF function in the cerebellar cortex, this thesis used optical imaging and single PCs recordings in the mouse cerebellar cortex, both in normal mice and in a murine model of a P/Q-type Ca<super>2+</super> channelopathy. The results provide the first demonstration of beam-like activation of PCs in the cerebellar cortex to peripheral input in normal mice. Furthermore, the pattern of PC responses depends on extracellular glutamate and its local regulation by excitatory amino acid transporters. The findings account for the contradictions of previous studies, clarifying why the responses in some regions of the cerebellar cortex are patch-like and other beam-like.Altered GC-PF-PC synaptic transmission is hypothesized to produce cerebellar motor dysfunction. This thesis tests this hypothesis in the tottering (<italic>tg/tg</italic>) mouse that has mutation in the gene that codes for the α1A pore-forming subunit of the P/Q-type voltage gated Ca<super>2+</super> channel and is a model for human episodic ataxia type 2 (EA2). This channel is highly expressed on both GCs and PCs. Further, both EA2 patients and <italic>tg/tg</italic> mice have cerebellar ataxia. The thesis shows that the GC-PF-PC synaptic transmission is reduced in the <italic>tg/tg</italic> mouse and a main pharmacological therapy for EA2, 4-aminopyridine, rescues the deficits. The results strongly implicate decreased GC-PF-PC function in the baseline ataxia. Both EA2 patients and <italic>tg/tg</italic> mice have non-episodic neurologic dysfunction, such as the cerebellar ataxia, but also episodic dysfunction. The episodic abnormalities involve the cerebral cortex, including epilepsy, migraine headaches and cognitive dysfunction. The final component of the thesis examined whether episodic abnormalities are present in the cerebral cortex of the <italic>tg/tg</italic> mouse. Optical imaging and single cell recording results demonstrate highly abnormal excitability changes throughout the cerebral cortex of <italic>tg/tg</italic> mice consisting of transient low frequency oscillations (LFOs) very high power. The LFOs are mediated, at least in part, by neuronal activity. Unexpectedly, the LFOs are driven by reducing excitatory inputs to the cerebral cortex. Furthermore, the high power LFOs are decreased markedly by acetazolamide and 4-aminopyridine, the primary treatments for EA2, demonstrating disease relevance. The LFOs in the tg/tg mouse represent an abnormal state involving decreased excitatory synaptic transmission and may underlie non-cerebellar symptoms that characterize P/Q-type Ca<super>2+</super> channelopathies.