Primates have several reflexes that generate eye movements to compensate for bodily movements that would otherwise disturb their gaze and undermine their ability to process visual information. Two vestibulo-ocular reflexes compensate selectively for rotational and translational disturbances of the head, and each has visual backups that operate as negative feedback tracking mechanisms to deal with any residual disturbances of gaze. Of particular interest here are three recently discovered visual tracking mechanisms that specifically address translational disturbances and operate in machine-like fashion with ultra-short latencies (< 60 ms in monkeys, < 85 ms in humans). These visual reflexes deal with motions in all three dimensions and operate as automatic servos, using preattentive parallel processing to provide signals that initiate eye movements before the observer is even aware that there has been a disturbance. This processing is accomplished by visual filters each tuned to a different feature of the binocular images located in the immediate vicinity of the plane of fixation. Two of the reflexes use binocular stereo cues and the third is tuned to particular patterns of optic flow associated with the observer's forward motion. Some stereoanomalous subjects show tracking deficits that can be attributed to a lack of just one subtype of cortical cell encoding motion in one particular direction in a narrow depth plane centred on fixation. Despite their rapid, reflex nature, all three mechanisms rely on cortical processing and evidence from monkeys supports the hypothesis that all are mediated by the medial superior temporal (MST) area of cortex. Remarkably, MST seems to represent the first stage in cortical motion processing at which the visual error signals driving each of the three reflexes are fully elaborated at the level of individual cells.