The motor system may use internal predictive models of the motor apparatus to achieve better control than would be possible by negative feedback. Several theories have proposed that the cerebellum may form these predictive representations. In this article, we review these theories and try to unify them by reference to an engineering control model known as a Smith Predictor. We suggest that the cerebellum forms two types of internal model. One model is a forward predictive model of the motor apparatus (e.g., limb and muscle), providing a rapid prediction of the sensory consequences of each movement. The second model is of the time delays in the control loop (due to receptor and effector delays, axonal conductances, and cognitive processing delays). This model delays a copy of the rapid prediction so that it can be compared in temporal register with actual sensory feedback from the movement. The result of this comparison is used both to correct for errors in performance and as a training signal to learn the first model. We discuss evidence that the cerebellum could form both of these models and suggest that the cerebellum may hold at least two separate Smith Predictors. One, in the lateral cerebellum, would predict the movement outcome in visual, egocentric, or peripersonal coordinates. Another, in the intermediate cerebellum, would predict the consequences in motor coordinates. Generalization of the Smith Predictor theory is discussed in light of cerebellar involvement in nonmotor control systems, including autonomic functions and cognition.