A powerful conceptual framework for the generation of fast, coordinated movements is based on the central nervous system implementing internal models. Internal models provide for representations of the input-output properties of the motor apparatus. There are two general classes of internal models. Forward models use the commands for an action and information about the present state to predict the consequences of that action. Inverse models transform a desired outcome or effector state into the necessary commands to achieve that state. It has been widely hypothesized that the cerebellum acquires and stores internal models. Initially formulated to explain the cerebellum’s role in motor control, the concept has been extended to include internal models for tool use and cognitive processes. In patients with cerebellar dysfunction, the deficits can be attributed to a failure of internal models to generate the appropriate model commands and/or to accurately estimate the consequences of motor commands. Functional imaging and transcranial magnetic stimulation studies in normal subjects provide further support for this hypothesis. Electrophysiological investigations have also examined whether neurons in the cerebellar cortex have the requisite signals compatible with either an inverse or forward internal model. In monkeys it remains uncertain whether the simple spike discharge of Purkinje cells has the requisite motor command signals required to be the output of an inverse dynamics model. However, Purkinje cell firing has several of the characteristics of a forward internal model. Furthermore, the function of cerebellar-like structures in several groups of electric fishes is to predict the sensory consequences of motor commands, suggesting that the cerebellar architecture can support the computations required by a forward model.