Our visual system is fundamentally retinotopic. When viewing a stable scene, each eye movement shifts object features and locations on the retina. Thus, sensory representations must be updated, or remapped, across saccades to align presaccadic and postsaccadic inputs. The earliest remapping studies focused on anticipatory, presaccadic shifts of neuronal spatial receptive fields. Over time, it has become clear that there are multiple forms of remapping and that different forms of remapping may be mediated by different neural mechanisms. This review attempts to organize the various forms of remapping into a functional taxonomy based on experimental data and ongoing debates about forward versus convergent remapping, presaccadic versus postsaccadic remapping, and spatial versus attentional remapping. We integrate findings from primate neurophysiological, human neuroimaging and behavioral, and computational modeling studies. We conclude by discussing persistent open questions related to remapping, with specific attention to binding of spatial and featural information during remapping and speculations about remapping's functional significance.