The first models that were proposed to account for the neural control of eye movements applied a classic control systems approach, including feedback, and measured system responses to sinusoidal and transient stimuli. Although such models provided many insights, their limitations were quickly recognized, such as their inability to account for anticipatory responses. Another question was whether models with lumped transfer functions could usefully represent a population of neurons, in which individual units were shown to encode a spectrum of different signals, including resting discharge rates and noise. Recent trends have been towards neural network models and Bayesian operators, which account for observed properties such as the variability of responses and predictive behavior, but often puzzle clinicians by their complexity and non-intuitive operations. We propose that, since all models are incomplete, it makes sense to select the simplest model that can address the topic of interest. We examine two aspects of abnormal ocular motor control, affecting the common integrator for eye movements, and the vestibular velocity storage mechanism. In both cases, we show how classic control systems provided substantial insights into clinical disorders—such as gaze-evoked nystagmus and periodic alternating nystagmus—as well as suggesting new questions, experiments, and potential treatments.