Recent progress in understanding the oculomotor system is briefly reviewed. This progress is largely due to technological advances such as the ability to record from neurons in behaving animals. Furthermore, parts of the oculomotor system are now well-enough understood that the techniques of exact science, such as quantitation and mathematical description, are becoming useful. This, in turn, leads to the use of the language of systems analysis, and the vestibulo-ocular reflex is examined as an example of such a description. Systems analysis not only organizes current knowledge but leads to predictions by way of hypotheses known as models. A model of time integration by neurons is given as an example. It is put forward to illustrate that our biggest problem at the moment is an inability to test such models at the neuronal network level.