Our sensory observations represent a delayed, noisy estimate of the environment. Delay causes instability and noise causes uncertainty. To deal with these problems, theory suggests that the processing of sensory information by the brain should be probabilistic: to start a movement or to alter it midflight, our brain should make predictions about the near future of sensory states and then continuously integrate the delayed sensory measures with predictions to form an estimate of the current state. To test the predictions of this theory, we asked participants to reach to the center of a blurry target. With increased uncertainty about the target, reach reaction times increased. Occasionally, we changed the position of the target or its blurriness during the reach. We found that the motor response to a given second target was influenced by the uncertainty about the first target. The specific trajectories of motor responses were consistent with predictions of a "minimum variance" state estimator. That is, the motor output that the brain programmed to start a reaching movement or correct it midflight was a continuous combination of two streams of information: a stream that predicted the near future of the state of the environment and a stream that provided a delayed measurement of that state.