People with profound memory deficits can acquire new motor skills, even though on each day of training they may be unaware of having seen the training apparatus before. Similarly, rabbits can acquire or retain a conditioned nictitating membrane response despite massive lesions of the hippocampus or the cerebral cortex. Both lines of evidence suggest that sub-cortical structures may be sufficient for many forms of motor learning. One possible locus for motor learning is the cerebellum. This article traces the history of our knowledge of structure and function of the cerebellum. The anatomical and physiological evidence demonstrates that the cerebellum has the neural connections necessary to mediate simple forms of motor learning or reflex plasticity. Behavioral studies demonstrate that the cerebellum is involved in modification of the vestibuloocular reflex, recalibration of saccadic eye movements, and acquisition of the conditioned nictitating membrane response. Although the evidence in all three instances suggests that the cerebellum is important, there is no agreement as to whether the cerebellum is always necessary for motor learning or how it might participate. Two views are presented: one supporting the idea of the cerebellum as the locus for motor learning and the other opposing this idea. Some evidence that might resolve these disagreements is discussed.