LTD has now been established as a synaptic plasticity specific to the cerebellum. Cellular and molecular mechanisms of LTD have been elucidated to some extent, but still a number of questions are left open. The most crucial question may concern its time course, as to how long the LTD lasts beyond the limit of the present maximum observation time of 3 hr, and whether and how it is eventually transformed to a permanent memory. Molecular mechanisms underlying LTD should be investigated further in respect to Ca2+ binding and storage, protein kinase C, phosphorylation of glutamate receptors, GTP proteins, etc. The ineffectiveness of mass field potentials in representing LTD makes such studies relatively difficult, and a hope for future development may be placed in reproduction of LTD in tissue cultured Purkinje cells or even in isolated glutamate receptors in a simplified form. The cerebellar neuronal network incorporating LTD as a memory element has been conceived as a simple perceptron-like (Albus 1971) or adaptive filter-like (Fujita 1982a) parallel processing computer. Such a neuronal computer incorporated in a reflex or a more complex movement system would endow the system with subtle capabilities of adaptation and learning. The scheme of the floccular control of the VOR closely resembles that of a self-tuning regulator, a type of adaptive control system. For cerebellar control of voluntary movements, however, another version of the adaptive control system, the model reference control system, seems to be more applicable (Ito 1986). This system continuously readjusts its dynamics by referring to errors derived through comparison of its performance with that of an internal model. It is important to note that a model for an unknown system can be built based on the same principle, by feeding errors derived from their comparison to adjust the model. It may thus be conceived that an internal model is built within the cerebellum in the manner of model reference adaptive control, and that an internal model so formed is utilized for adaptive control of movement. A recent simulation study successfully reproduced learning in formation of an arm trajectory based on these principles of model reference control (Kawato et al 1987). On the experimental side, however, the complex neural organization for control of locomotion, posture, and voluntary movements still eludes full elucidation. Nevertheless, evidence is accumulating to support the cerebellar learning hypothesis.(ABSTRACT TRUNCATED AT 400 WORDS)