Internal models are a key feature of most modern theories of motor control. Yet, it has been challenging to localize internal models in the brain, or to demonstrate that they are more than a metaphor. In the present review, I consider a large body of data on the cerebellar floccular complex, asking whether floccular output has features that would be expected of the output from internal models. I argue that the simple spike firing rates of a single group of floccular Purkinje cells could reflect the output of three different internal models. (1) An eye velocity positive feedback pathway through the floccular complex provides neural inertia for smooth pursuit eye movements, and appears to operate as a model of the inertia of real-world objects. (2) The floccular complex processes and combines input signals so that the dynamics of its average simple spike output are appropriate for the dynamics of the downstream brainstem circuits and eyeball. If we consider the brainstem circuits and eyeball as a more broadly conceived "oculomotor plant," then the output from the floccular complex could be the manifestation of an inverse model of "plant" dynamics. (3) Floccular output reflects an internal model of the physics of the orbit where head and eye motion sum to produce gaze motion. The effects of learning on floccular output suggest that it is modeling the interaction of the visually-guided and vestibular-driven components of eye and gaze motion. Perhaps the insights from studying oculomotor control provide groundwork to guide the analysis of internal models for a wide variety of cerebellar behaviors.