This paper reviews major trends in the study of the oculomotor system since Westheimer published his doctoral research on this topic 35 years ago. Westheimer introduced the use of linear system analysis for the study of eye movements, an approach used a great deal by others ever since. Westheimer himself abandoned this approach within a decade, in part, because this kind of analysis becomes ambiguous when predictive properties of oculomotor system performance become prominent. We discuss the implications of ignoring the prominence of predictive eye movements and describe recent evidence for their prevelance and power. This leads us to propose that a new approach to the study of oculomotor performance is required. We also discuss the recent trend to apply the "connectionist" (or "neural network") approach in studies of the oculomotor system, and point out that the "symbolic", rather than the "adaptive", nature of predictive eye movements makes successful extension of these models to oculomotor performance unlikely. Our new approach emphasizes the use of natural stimulation in subjects free from bodily restraints. Accurate measurement of eye, head and torso movements under such conditions has become possible recently and data obtained in this manner has led to the discovery of a number of unexpected characteristics of oculomotor system performance. These developments have encouraged us to abandon the modular view of the oculomotor system, popular since Dodge launched the modern era of oculomotor research in 1903, which postulates five, or more, largely independent "subsystems". We suggest that only two subsystems (a fast saccadic and a somewhat slower smooth) are used to fixate and track a central representation of objects located in three-dimensional space. We show that this two-subsystem approach is consistent with current knowledge of oculomotor system neuroanatomy and neurophysiology. © 1990.