Although one particular model of the cerebellum, as proposed by Marr and Albus, provides a formal framework for understanding how heterosynaptic plasticity of Purkinje cells might be used for motor learning, the physiological details remain largely an engima. Developments in computational neuroscience and artificial neural networks applied to real control problems are essential to understand fully how workspace errors associated with movement performances can be converted into motor-command errors, and how these errors can then be used as one kind of synaptic input by motor-learning algorithms that are based on biologically plausible rules involving heterosynaptic plasticity. These developments, as well as recent advances in the study of cellular mechanisms of synaptic plasticity, form the basis for the detailed computational models of cerebellar motor learning that have been proposed. These models provide hints toward resolving a long-standing controversy in the oculomotor literature regarding the sites of adaptive changes in the vestibuloocular reflex (VOR) and the optokinetic eye movement response (OKR), and suggest new experiments to elucidate general mechanisms of sensory motor learning.