Sleep and wake states are regulated by the coordinated activity of neuronal populations in the brainstem and hypothalamus. Synaptic interactions among these populations define sleep-wake regulatory networks; however, the structure and dynamics of these networks, particularly with respect to the regulation of rapid eye movement (REM) sleep, are not well understood. We have developed a mathematical modeling framework that is uniquely suited for investigating the dynamics of sleep-wake regulation. I will discuss our analysis of network dynamics and the interplay between deterministic and stochastic model properties in the production of physiological sleep-wake behavior.