Abstract Models have become a major tool in oculomotor physiology as a means of interpreting experimental results, formulating hypotheses, and understanding system function. Basically, a model is set of mathematical equations describing the theoretical or empirical relationship between the various physical and/or conceptual variables characterizing a system. In oculomotor physiology these equations are generally represented in the form of signal flow diagrams which are manipulated and analyzed using the inventory of systems control theory. We here distinguish between conceptual models sketching the direction and qualitative character of interactions between the constituents of a system, descriptive models summarizing empirical observations, inferential models inferring a system's internal structure from input-output measurements, and homeomorphic models reflecting all of a system's essential components and their actual arrangement. Early models of the saccadic and the smooth pursuit systems, and their subsequent evolution and contribution to current views, are considered in some detail. A basic problem of these systems (and of any other visuomotor system) is the appreciable transport delay enclosed by the retinal feedback loop which can lead to instability (oscillations). Whereas it is well established that the saccadic system obviates this problem in most situations by its discontinuous operation, the principle adopted by the pursuit system is still debated.