Motor cortex in the primate brain controls movement at a complex level. For example, electrical stimulation of motor cortex on a behavioral time scale can elicit multi-joint movements that resemble common gestures in the monkey’s behavioral repertoire. How is this complex control accomplished? It was once hypothesized that motor cortex contains a topographic, one-to-one map from points in cortex to muscles. It is now well known that the topography contains a considerable degree of overlap and that the mapping between points in cortex and muscles is many-to-many. However, can a fixed, many-to-many map account for the complex manner in which motor cortex appears to control movement? Recent experiments suggest that the mapping between cortex and muscles may be of a higher order than a fixed, many-to-many map; it may continuously change depending on proprioceptive feedback from the limb. This “feedback remapping” may be a fundamental aspect of motor control, allowing motor cortex to flexibly control almost any high-level or low-level aspect of movement.