Sensory and motor uncertainty form fundamental constraints on human sensorimotor control. I will first show that the CNS reduces the uncertainty in estimates about the state of the world by using a Bayesian combination of prior knowledge with an estimate of the uncertainty of its own sensors. I will then describe how prediction of the consequences of our actions can be used to reduce uncertainty and present experiments on tickling and force escalation which elucidate the predictive mechanisms. Finally, I will describe how signal-dependent noise on the motor output places constraints on performance. Given these constraints features of goal-directed movement arise from a model in which the statistics of our actions are optimized. Together these studies provide a probabilistic framework for sensorimotor control.