Although many functions have been ascribed to the cerebellum, the uniformity of its synaptic organization suggests that a single, characteristic computation may be common to all. Computer simulations are useful in examining this cerebellar computation, as they inherently address function at the level of information processing. Progress is facilitated by factors that make the cerebellum particularly amenable to such analysis. We review progress from two contrasting approaches. Top-down simulations begin with hypotheses about computational mechanisms and then ask how such mechanisms might operate within the cerebellum. Bottom-up simulations attempt to build a representation of the cerebellum that reflects known cellular and synaptic components as accurately as possible. We describe recent advances from these two approaches that are leading to an understanding of what information the cerebellum processes and how its neurons and synapses accomplish this task.