Sensory and motor uncertainty form fundamental constraints on human performance. 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 the brain evaluates errors in terms of a loss function. 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.