Motor control is the study of how organisms make accurate goal-directed movements. Here we consider two problems that the motor system must solve in order to achieve such control. The first problem is that sensory feedback is noisy and delayed, which can make movements inaccurate and unstable. The second problem is that the relationship between a motor command and the movement it produces is variable, as the body and the environment can both change. A solution is to build adaptive internal models of the body and the world. The predictions of these internal models, called forward models because they transform motor commands into sensory consequences, can be used to both produce a lifetime of calibrated movements, and to improve the ability of the sensory system to estimate the state of the body and the world around it. Forward models are only useful if they produce unbiased predictions. Evidence shows that forward models remain calibrated through motor adaptation: learning driven by sensory prediction errors.