This chapter reviews evidence demonstrating the essential role of the cerebellum and its associated circuitry in the learning and memory of classical conditioning of discrete behavioral responses (e.g., eyeblink, limb flexion, head turn). It now seems conclusive that the memory traces for this basic category of associative learning are formed and stored in the cerebellum. Lesion, neuronal recording, electrical microstimulation, and anatomical procedures have been used to identify the essential conditioned stimulus (CS) circuit, including the pontine mossy fiber projections to the cerebellum; the essential unconditioned stimulus (US) reinforcing or teaching circuit, including neurons in the inferior olive (dorsal accessory olive) projecting to the cerebellum as climbing fibers; and the essential conditioned response (CR) circuit, including the interpositus nucleus, its projection via the superior cerebellar peduncle to the magnocellular red nucleus, and rubral projections to premotor and motor nuclei. Each major component of the eyeblink CR circuit was reversibly inactivated both in trained animals and over the course of training. In all cases in trained animals, inactivation abolished the CR (and the UR as well when motor nuclei were inactivated). When animals were trained during inactivation (and not exhibiting CRs) and then tested without inactivation, animals with inactivation of the motor nuclei, red nucleus, and superior peduncle had fully learned, whereas animals with inactivation of a very localized region of the cerebellum (anterior interpositus and overlying cortex) had not learned at all. Consequently, the memory traces are formed and stored in the cerebellum. Several alternative possibilities are considered and ruled out. Both the cerebellar cortex and the interpositus nucleus are involved in the memory storage process, suggesting that a phenomenon-like long-term depression (LTD) is involved in the cerebellar cortex and long-term potentiation (LTP) is involved in the interpositus. The experimental findings reviewed in this chapter provide perhaps the first conclusive evidence for the localization of a basic form of memory storage to a particular brain region, namely the cerebellum, and indicate that the cerebellum is indeed a cognitive machine.