Neuroscience is just beginning to understand the neural computations that underlie our remarkable capacity to learn new motor tasks. Studies of natural movements have emphasized the importance of concepts such as dimensionality reduction within hierarchical levels of redundancy, optimization of behavior in the presence of sensorimotor noise and internal models for predictive control. These concepts also provide a framework for understanding the improvements in performance seen in myoelectric-controlled interface and brain-machine interface paradigms. Recent experiments reveal how volitional activity in the motor system combines with sensory feedback to shape neural representations and drives adaptation of behavior. By elucidating these mechanisms, a new generation of intelligent interfaces can be designed to exploit neural plasticity and restore function after neurological injury.