Gerald Westheimer has made diverse and important discoveries about the visual system over the past 60 years. These include: the mathematical analysis of disjunctive eye movements as a control system — an analysis with the greatest predictive power so far achieved on a biological system of this type; objective determination of the quality of the retinal image; the influence of the cerebellum on eye movements in primates; the mechanism for achieving high positional accuracy in vision (hyperacuity); and the reasons for the small effect of image motions on this ability.