The cellular and ionic mechanisms that generate the rhythm in central pattern generator (CPG) networks for simple movements are not well understood. Using vertebrate locomotion, respiration and mastication as exemplars, I describe four main principles of rhythmogenesis: (1) rhythmogenic ionic currents underlie all CPG networks, regardless of whether they are driven by a network pacemaker or an endogenous pacemaker neuron kernel; (2) fast synaptic transmission often evokes slow currents that can affect cycle frequency; (3) there are likely to be multiple and redundant mechanisms for rhythmogenesis in any essential CPG network; and (4) glial cells may participate in CPG network function. The neural basis for rhythmogenesis in simple behaviors has been studied for almost 100 years, yet we cannot identify with certainty the detailed mechanisms by which rhythmic behaviors are generated in any vertebrate system. Early studies focused on whether locomotor rhythms were generated by a chain of coupled reflexes that require sensory feedback, or by a central neural network. By now there is general agreement that for the major rhythmic behaviors (including locomotion, respiration, and mastication, the subjects of this book), there exist CPG networks within the central nervous system that are able to drive the basic rhythmic behavior in the complete absence of sensory feedback. This of course does not eliminate an important role for sensory feedback, which certainly affects cycle frequency and for some behaviors determines the timing of one phase of the behavior (Borgmann et al., 2009; Pearson, 2008). Given the existence of CPGs, the question of rhythmogenesis can be rephrased to ask how these networks determine the timing of the rhythmic behavior. In this chapter, I focus on cellular and molecular mechanisms that could underlie rhythmogenesis in CPG networks, especially those that drive locomotion, respiration, and mastication.