Traditionally, clinicians have used their experience and intuition to diagnose and treat disease states, including neurological disorders. However, the rapid increase in basic knowledge, coupled with a realization that human judgments are often flawed, has made it helpful to approach many clinical disorders by casting them in the form of models (quantitative hypotheses) that can be tested experimentally; in this way the power of the scientific method can be applied. This is especially the case in systems neuroscience, in which the experimental testing of mathematical models has proven an effective approach to understanding a range of clinical problems. Here, we focus on disorders of the neural control of eye movements, which offer many advantages to clinician scientists, providing examples of how thorny clinical mysteries became much clearer once they were formulated as models, and tested experimentally. Such an approach inevitably raises new questions and experimental tests and may suggest novel therapies.