The comparative methods of evolutionary biology are a useful tool for investigating the functions of sleep. These techniques can help determine whether experimental results, derived from a single or few species, apply broadly across a specified group of animals. In this way, comparative analysis is a powerful complement to experimentation. The variation in the time mammalian species spend asleep has been most amenable for use with this approach, given the large number of mammals for which sleep data exist. Here, it is assumed that interspecific variation in the time spent asleep reflects underlying differences in the need for sleep. If true, then significant predictors of sleep times should provide insight into the function of sleep. Many such analyses have sought the evolutionary determinants of mammalian sleep by relating the time spent in the two basic states of sleep, rapid eye movement (REM) and non-REM sleep, to constitutive variables thought to be functionally related to sleep. However, the early analyses had several methodological problems, and recent re-analyses have overturned some widely accepted relationships, such as the idea that species with higher metabolic rates engage in more sleep. These more recent studies also provide evolutionarily broad support for a neurophysiological role for REM sleep. Furthermore, results from comparative analyses suggest that animals are particularly vulnerable to predation during REM sleep, a finding that lends further support to the notion that REM sleep must serve an important function. Here, we review the methodology and results of quantitative comparative studies of sleep. We highlight important developments in our understanding of the evolutionary determinants of sleep and emphasize relationships that address prevailing hypotheses for the functions of sleep. Lastly, we outline a possible future for comparative analyses, focusing on work in non-mammalian groups, the use of more physiologically meaningful variables, and electrophysiological sleep studies conducted in the wild.