How visual space is represented in the brain is an open question in neuroscience. Embodiment theories propose that spatial perception is structured by neural motor maps. Especially, maps which code the targets for saccadic eye movements contain a precise representation of external space. In this review article, we examine how modifications in saccade maps are accompanied by changes in visual space perception. Saccade adaptation, a method which systematically modifies saccade amplitudes, alters the localization of visual objects in space. We illustrate how information about saccade amplitudes is transferred from the cerebellum (CB) to the frontal eye field (FEF). We argue that changes in visual localization after adaptation of saccade maps provide evidence for a shared representation of visual and motor space.