At every moment, the image the world projects on our eyes undergoes rapid and dramatic changes due to the eye movements and to the motion of the objects. Surprisingly, we are not aware of these changes, experiencing the world as stable and constant. This apparent contradiction suggests that our visual system uses non-retinotopic representations of the objects in the visual scene to create a stable percept of the world. Which visual mechanisms make use of non-retinotopic representations is a question of fundamental importance in neuroscience. The study of visual stability and non-retinotopic processing has classically focused on the problem of eye movements and has been studied in this context. We have proposed a new view on the problem of non-retinotopic processing that allows explaining how a stable percept of the world is created both across the movements of the eyes and objects. Based on this view, we devised an experimental paradigm that allows testing whether a given mechanism makes use of non-retinotopic representations and we applied it to several different visual processes. Our results suggest that non-retinotopic representations are used in higher-level visual processes whereas low-level mechanisms seem to operate on retinotopic representations.