Vision is an active process. We do not see the world directly; rather, we construct a representation of it from sensory inputs in combination with internal, nonvisual signals. In the case of spatial perception, our representation of the visual scene must take into account our own movements. This allows us to perceive the world as stationary despite the constant eye movements that produce new images on the retina. How is this perceptual stability achieved? Our central hypothesis is that a corollary discharge of the eye movement command updates, or remaps, an internal representation when the eyes move. In support of this hypothesis, the authors review evidence that parietal cortex and extrastriate visual areas in both monkeys and humans participate in spatial updating. These findings shed new light on the neural circuitry involved in producing a stable and coherent perception of visual space.