Recent data of neuronal network structures of the cerebellum are reviewed and experimental evidence is presented for the hypothesis that parallel fiber synapses on Purkinje cells retain plasticity which provides a memory device to the cerebellar cortical network. A corticonuclear microcomplex, consisting of a small area of the cerebellar cortex, a small group of cerebellar and vestibular nuclear neurons, and a small group of inferior olive neurons, which are interconnected, is proposed to form a functional unit of the cerebellum. The idea that a corticonuclear microcomplex endows an extracerebellar system with subtle control capabilities such as coordination, prediction, and adaptation-learning is supported with experimental data on the cerebellar control of the vestibulo-ocular reflex.