Visual neurons typically receive information from a limited portion of the retina, and such receptive fields are a key organizing principle for much of visual cortex. At the same time, there is strong evidence that receptive fields transiently shift around the time of saccades. The nature of the shift is controversial: Previous studies have found shifts consistent with a role for perceptual constancy; other studies suggest a role in the allocation of spatial attention. Here we present evidence that both the previously documented functions exist in individual neurons in primate cortical area V4. Remapping associated with perceptual constancy occurs for saccades in all directions, while attentional shifts mainly occur for neurons with receptive fields in the same hemifield as the saccade end point. The latter are relatively sluggish and can be observed even during saccade planning. Overall these results suggest a complex interplay of visual and extraretinal influences during the execution of saccades.