We often gaze at and attend to an object while preparing to reach toward and grasp it, and continue doing so when the plan is executed. Elaborate machinery, much of it in the brainstem and spinal cord, provides control systems for the spatially congruent guidance of the eyes, limbs, and body toward targets in visual space. We will use the term standard mapping for the sensorimotor transformations that underlie such behavior. Despite the common sense character of standard mapping, the targets of gaze, attention, and reaching can be dissociated from each other. We can attend to stimuli in locations that differ from the target of action. We can gaze in one direction while reaching in another. And we can guide spatial action with nonspatial stimuli, such as when, in conditional motor tasks, the color of an object instructs a movement elsewhere in space. All of these situations, and many others, call for a process that we term nonstandard mapping, wherein the central nervous system must reject the commonplace correspondences among visuospatial stimuli, gaze, attention, and reaching movements. We focus in this article on the possibility that premotor cortex underlies nonstandard mapping and, therefore, the behavioral flexibility that such a process allows.