Central Pattern Generators (CPGs) are limited neural networks that drive rhythmic behaviors such as locomotion, respiration and mastication. We have been studying the structure, function, and modulation of CPGs, with an emphasis on neuronal and ionic mechanisms that allow flexibility in the output from an anatomically defined network. Both biological and modeling studies show that individual oscillatory neurons can be modulated to generate bursting activity by a variety of independent ionic mechanisms, allowing flexibility in the frequency and output properties of these important neurons. The phasing of neuronal activity in the rhythmic pattern is not determined only by the pattern of synaptic connections; the intrinsic electrophysiological properties of the neurons also play a major role. These points raise issues with regard to the appropriate level of complexity in models of neural networks. I will discuss these issues based on work done in collaboration with John Guckenheimer on the pyloric network in the crustacean stomatogastric ganglion and the rodent spinal locomotor CPG. Supported by NIH grants NS17323, NS050943 and NSF grant IOS-0749467