When details of neuronal network structures of the cerebellum were uncovered in the 1960's, a hope emerged that functions of the cerebellum would eventually be explained in terms of operation of the cerebellar neuronal network. While various network models were proposed, involvement of synaptic plasticity in the cerebellar neuronal network as a memory process became a focus of discussion. The characteristic dual inputs to Purkinje cells, one from parallel fibers (axons of granule cells) and the other from climbing fibers, were suggested to represent such synaptic plasticity, and under this assumption, the cerebellar cortex was envisaged as a learning machine for pattern recognition. Despite these theoretical suggestions, earlier efforts to reveal the postulated synaptic plasticity in the cerebellar cortex were unsuccessful. It had then to wait for a decade before long-term depression (LTD) was finally found as its possible substrate. LTD is a long-lasting depression of parallel fiber-to-Purkinje cell transmission that occurs following conjunctive activation of parallel fibers and a climbing fiber both converging onto one and the same Purkinje cell. LTD has now been established by means of various testing methods, and recent efforts have been directed toward its molecular mechanisms. Efforts have also been devoted to demonstrate roles of LTD in motor learning through studies of adaptation of the vestibulo-ocular reflex, adaptive adjustment of hand movement, and more recently eyelid blink conditioned reflex. This article reviews recent efforts to characterize the LTD as a memory process, presumably the major, in the cerebellum.