Sleep is a pervasive characteristic of mammalian species, yet its purpose remains obscure. It is often proposed that 'sleep is for the brain', a view that is supported by experimental studies showing that sleep improves cognitive processes such as memory consolidation. Some comparative studies have also reported that mammalian sleep durations are higher among more encephalized species. However, no study has assessed the relationship between sleep and the brain structures that are implicated in specific cognitive processes across species. The hippocampus, neocortex and amygdala are important for memory consolidation and learning and are also in a highly actived state during sleep. We therefore investigated the evolutionary relationship between mammalian sleep and the size of these brain structures using phylogenetic comparative methods. We found that evolutionary increases in the size of the amygdala are associated with corresponding increases in NREM sleep durations. These results are consistent with the hypothesis that NREM sleep is functionally linked with specializations of the amygdala, including perhaps memory processing.