Uncertainty constitutes a fundamental constraint on human sensorimotor control. Our sensors are noisy and do not provide perfect information about all the properties of the world. Moreover, our muscles generate noisy outputs and many tasks we perform vary in an unpredictable way. Here we review the computations that the CNS uses in the face of such sensory, motor and task uncertainty. We show that the CNS reduces the uncertainty in estimates about the state of the world by using a Bayesian combination of prior knowledge and sensory feedback. It is shown that these mechanisms generalize to state estimation of ones own body during movement. We review how the CNS optimizes decisions based on these estimates, examining the error criterion that people optimize when performing targeted movements. Finally, we describe how signal-dependent noise on the motor output places constraints on performance. Goal-directed movement arises from a model in which the statistics of our actions are optimized. Together these studies provide a probabilistic framework for sensorimotor control.