When we use a novel tool, the motor commands may not produce the expected outcome. In healthy individuals, with practice the brain learns to alter the motor commands. This change depends critically on the cerebellum as damage to this structure impairs adaptation. However, it is unclear precisely what the cerebellum contributes to the process of adaptation in human motor learning. Is the cerebellum crucial for learning to associate motor commands with novel sensory consequences, called forward model, or is the cerebellum important for learning to associate sensory goals with novel motor commands, called inverse model? Here, we compared performance of cerebellar patients and healthy controls in a reaching task with a gradual perturbation schedule. This schedule allowed both groups to adapt their motor commands. Following training, we measured two kinds of behavior: in one case, people were presented with reach targets near the direction in which they had trained. The resulting generalization patterns of patients and controls were similar, suggesting comparable inverse models. In the second case, participants reached without a target and reported the location of their hand. In controls, the pattern of change in reported hand location was consistent with simulation results of a forward model that had learned to associate motor commands with new sensory consequences. In patients, this change was significantly smaller. Therefore, in our sample of patients, we observed that while adaptation of motor commands can take place despite cerebellar damage, cerebellar integrity appears critical for learning to predict visual sensory consequences of motor commands.