Rationality principles such as optimal feedback control and Bayesian inference underpin a probabilistic framework that has accounted for a range of empirical phenomena in biological sensorimotor control. To facilitate the optimization of flexible and robust behaviors consistent with these theories, the ability to construct internal models of the motor system and environmental dynamics can be crucial. In the context of this theoretic formalism, we review the computational roles played by such internal models and the neural and behavioral evidence for their implementation in the brain.