Feed forward control and estimates of the future state of the motor system are critical for fast and coordinated movements. One framework for generating these predictive signals is based on the central nervous system implementing internal models. Internal models provide for representations of the input-output properties of the motor apparatus or their inverses. It has been widely hypothesized that the cerebellum acquires and stores internal models of the motor apparatus. The results of psychophysical, functional imaging and transcranial magnetic stimulation studies in normal subjects support this hypothesis. Also, the deficits in patients with cerebellar dysfunction can be attributed to a failure of predictive feed forward control and/or to accurately estimate the consequences of motor commands. Furthermore, the computation performed by the cerebellar-like electrosensory lobes in several groups of fishes is to predict the sensory consequences of motor commands. However, only a few electrophysiological investigations have directly tested whether neurons in the cerebellar cortex have the requisite signals compatible with either an inverse or forward internal model. Our studies in the monkey performing manual pursuit tracking demonstrate that the simple spike discharge of Purkinje cells does not have the dynamics-related 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 of the arm. A synthesis of the evidence suggests that the cerebellum is involved in integrating the current state of the motor system with internally generated motor commands to predict the future state.