Motor learning is a very basic, essential form of learning that appears to share common mechanisms across different motor systems. We evaluate and compare a few conceptual models for learning in a relatively simple neural system, the vestibulo-ocular reflex (VOR) of vertebrates. We also compare the different animal models that have been used to study the VOR. In the VOR, a sensory signal from the semicircular canals is transformed into a motor signal that moves the eyes. The VOR can modify the transformation under the guidance of vision. The changes are persistent and share some characteristics with other types of associative learning. The cerebellar cortex is directly linked to the VOR reflex circuitry in a partnership that is present in all vertebrates, and which is necessary for motor learning. Early theories of Marr, Albus, and Ito, in which motor memories are stored solely in the cerebellar cortex, have not explained the bulk of the experimental data. Many studies appear to indicate a site of learning in the vestibular nuclei, and the most successful models have incorporated long-term memory storage in both the cerebellar cortex and the brainstem. Plausible cellular mechanisms for learning have been identified in both structures. We propose that short-term motor memory is initially stored in the cerebellar cortex, and that during consolidation of the motor memory the locus of storage shifts to include a brainstem site. We present experimental results that support our hypothesis.