When the brain generates a motor command, it also predicts the sensory consequences of that command via an "internal model". The reliance on a model appears to make the brain able to sense the world better than is possible from the sensors alone. However, this happens only when the models are accurate. To keep the models accurate, the brain must constantly learn from prediction errors. Here I use examples from saccade and reach adaptation to demonstrate that learning is guided by multiple timescales: a fast system that strongly responds to error but rapidly forgets, and a slow system that weakly responds to error but has good retention.