The fundamental role of the visual system is to guide behavior in natural environments. To optimize information transmission, many animals have evolved a non-homogeneous retina and serially sample visual scenes by saccadic eye movements. Such eye movements, however, introduce high-speed retinal motion and decouple external and internal reference frames. Until now, these processes have only been studied with unnatural stimuli, eye movement behavior, and tasks. These experiments confound retinotopic and geotopic coordinate systems and may probe a non-representative functional range. Here we develop a real-time, gaze-contingent display with precise spatiotemporal control over high-definition natural movies. In an active condition, human observers freely watched nature documentaries and indicated the location of periodic narrow-band contrast increments relative to their gaze position. In a passive condition under central fixation, the same retinal input was replayed to each observer by updating the video's screen position. Comparison of visual sensitivity between conditions revealed three mechanisms that the visual system has adapted to compensate for peri-saccadic vision changes. Under natural conditions we show that reduced visual sensitivity during eye movements can be explained simply by the high retinal speed during a saccade without recourse to an extra-retinal mechanism of active suppression; we give evidence for enhanced sensitivity immediately after an eye movement indicative of visual receptive fields remapping in anticipation of forthcoming spatial structure; and we demonstrate that perceptual decisions can be made in world rather than retinal coordinates.