Sleep occupies a third of our life and is a primary need for all animal species studied so far. Nonetheless, chronic sleep restriction is a growing source of morbidity and mortality in both developed and developing countries. Sleep loss is associated with the subjective feeling of sleepiness and with decreased performance, as well as with detrimental effects on general health, cognition, and emotions. The ideas that small brain areas can be asleep while the rest of the brain is awake and that local sleep may account for at least some of the cognitive and behavioral manifestations of sleepiness are making their way into the scientific community. We herein clarify the different ways sleep can intrude into wakefulness, summarize recent scientific advances in the field, and offer some hypotheses that help framing sleepiness as a local phenomenon.