Cerebellar Purkinje cells exhibit a unique type of synaptic plasticity, namely, long-term depression (LTD). When two inputs to a Purkinje cell, one from a climbing fiber and the other from a set of granule cell axons, are repeatedly associated, the input efficacy of the granule cell axons in exciting the Purkinje cell is persistently depressed. Section I of this review briefly describes the history of research around LTD, and section II specifies physiological characteristics of LTD. Sections III and IV then review the massive data accumulated during the past two decades, which have revealed complex networks of signal transduction underlying LTD. Section III deals with a variety of first messengers, receptors, ion channels, transporters, G proteins, and phospholipases. Section IV covers second messengers, protein kinases, phosphatases and other elements, eventually leading to inactivation of DL-alpha-amino-3-hydroxy-5-methyl-4-isoxazolone-propionate-selective glutamate receptors that mediate granule cell-to-Purkinje cell transmission. Section V defines roles of LTD in the light of the microcomplex concept of the cerebellum as functionally eliminating those synaptic connections associated with errors during repeated exercises, while preserving other connections leading to the successful execution of movements. Section VI examines the validity of this microcomplex concept based on the data collected from recent numerous studies of various forms of motor learning in ocular reflexes, eye-blink conditioning, posture, locomotion, and hand/arm movements. Section VII emphasizes the importance of integrating studies on LTD and learning and raises future possibilities of extending cerebellar research to reveal memory mechanisms of implicit learning in general.