On July 1st 2005 Science published its 125th anniversary issue and highlighted the most compelling but unresolved scientific questions. Why we sleep and why we dream were two of them. This paper will first present a logical construct derived from evolutionary theory that any explanation of sleep must be able to fit in order to be applicable to diverse organisms across the tree of life. This construct is then used to satisfy the identification of the primary function of sleep (defined as the reason that sleep evolved for the function it still serves), and distinguishes this from secondary functions (defined as those that are associated with sleep but which are not part of its fundamental nature). Identification of the primary adaptive property of sleep that is visible to natural selection is then used to explain how sleep powerfully affects the individual fitness of organisms and the evolutionary trajectory of species. This identification of the primary function of sleep explains the diversity of sleep-wake behaviour between species and individuals across the lifespan, and the consequences of sleep disruption and drug-induced sedation on brain activity and behaviour.