Sleep is vital to cognitive performance, productivity, health and well-being. Earlier theories of sleep presumed that it occurred at the level of the whole organism and that it was governed by central control mechanisms. However, evidence now indicates that sleep might be regulated at a more local level in the brain: it seems to be a fundamental property of neuronal networks and is dependent on prior activity in each network. Such local-network sleep might be initiated by metabolically driven changes in the production of sleep-regulatory substances. We discuss a mathematical model which illustrates that the sleep-like states of individual cortical columns can be synchronized through humoral and electrical connections, and that whole-organism sleep occurs as an emergent property of local-network interactions.