We are estimated to spend one third of our life asleep, and it is increasingly apparent that good sleep is essential for overall health. Yet many people suffer from insufficient sleep or sleep disorders. Even though there is only a partial understanding about the why and how of sleep, mathematical models do exist that capture the broad features of sleep-wake regulation and are widely used in safety-critical industries to model fatigue risk. In this talk we will discuss some mathematical models of sleep-wake regulation and their multi-time scale features. Most mathematical models consider two states: a sleep and a wake state. However, the two state models do not account for the fact that during the night we cycle between two main sleep states (rapid eye movement (REM) and non-rapid eye movement (NREM) sleep). We will also discuss a model that considers three states: these two sleep states and a wake state. We will show that this model can be considered as a three-timescale problem. This three-timescale decomposition reveals additional geometric structure which acts to organise oscillations between REM and NREM states. This deeper geometric understanding of the generation of REM-NREM cycles brings insight into the relationship between model predicted and observed patterns of REM-NREM cycles and suggests ways in which models could be modified to more accurately reflect patterns of human sleep. This is joint research with Anne Skeldon, Derk Jan Dijk, Rachel Bernasconi, Matthew Bailey, Panos Kaklamanos, and Paul Glendinning.