There are now a reasonable number of invertebrate central pattern generator (CPG) circuits described in sufficient detail that a mechanistic explanation of how they work is possible. These small circuits represent the best-understood neural circuits with which to investigate how cell-to-cell synaptic connections and individual channel conductances combine to generate rhythmic and patterned output. In this review, some of the main lessons that have appeared from this analysis are discussed and concrete examples of circuits ranging from single phase to multiple phase patterns are described. While it is clear that the cellular components of any CPG are basically the same, the topology of the circuits have evolved independently to meet the particular motor requirements of each individual organism and only a few general principles of circuit operation have emerged. The principal usefulness of small systems in relation to the brain is to demonstrate in detail how cellular infrastructure can be used to generate rhythmicity and form specialized patterns in a way that may suggest how similar processes might occur in more complex systems. But some of the problems and challenges associated with applying data from invertebrate preparations to the brain are also discussed. Finally, I discuss why it is useful to have well-defined circuits with which to examine various computational models that can be validated experimentally and possibly applied to brain circuits when the details of such circuits become available.