Visual motion perception is vital for survival. Single-unit recordings in primate primary visual cortex (V1) have revealed the existence of specialized motion sensing neurons; perceptual effects such as the motion after-effect demonstrate their importance for motion perception. Human psychophysical data on motion detection can be explained by a computational model of cortical motion sensors. Both psychophysical and physiological data reveal at least two classes of motion sensor capable of sensing motion in luminance-defined and texture-defined patterns, respectively. Psychophysical experiments also reveal that motion can be seen independently of motion sensor output, based on attentive tracking of visual features. Sensor outputs are inherently ambiguous, due to the problem of univariance in neural responses. In order to compute stimulus direction and speed, the visual system must compare the responses of many different sensors sensitive to different directions and speeds. Physiological data show that this computation occurs in the visual middle temporal (MT) area. Recent psychophysical studies indicate that information about spatial form may also play a role in motion computations. Adaptation studies show that the human visual system is selectively sensitive to large-scale optic flow patterns, and physiological studies indicate that cells in the middle superior temporal (MST) area derive this sensitivity from the combined responses of many MT cells. Extraretinal signals used to control eye movements are an important source of signals to cancel out the retinal motion responses generated by eye movements, though visual information also plays a role. A number of issues remain to be resolved at all levels of the motion-processing hierarchy. WIREs Cogni Sci 2011 2 305-314 DOI: 10.1002/wcs.110 For further resources related to this article, please visit the WIREs website Additional Supporting Information may be found in http://www.lifesci.sussex.ac.uk/home/George_Mather/Motion/index.html.