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The use of mathematical models of the human pilot in analyses of the pilot/vehicle system has brought a new dimension to the engineering treatment of flying qualities, stability and control, pilot/vehicle integration, and display system considerations. As an introduction to such models, elementary concepts and specific physical examples are used to set the stage for a step-by-step development of what is known about the human pilot as a dynamic control component. In the process, quasi-linear models for single-loop systems with visual stimuli and multiloop systems with visual stimuli are presented and then extended to cover multiloop, multi-modality situtations. Empirical connections between the pilot dynamics and pilot ratings are also considered. Some of the most important nonlinear features of human pilot behavior in adapting to changes in the character of the stimuli are described and tied to the quasi-linear models.