Sleep is homeostatically regulated in all species that have been carefully studied. In mammals and birds, the best characterized marker of sleep pressure is slow wave activity (SWA), defined as the electroencephalogram (EEG) power between 0.5 and 4 Hz during NREM sleep. SWA peaks at sleep onset and decreases with time spent asleep, and reflects the synchronous firing of cortical neurons coordinated by an underlying slow oscillation, the fundamental cellular phenomenon of NREM sleep. We have recently proposed the synaptic homeostasis hypothesis of sleep, which claims that an important function of sleep is to maintain synaptic balance. This hypothesis states that plastic processes during wake are biased towards synaptic potentiation, resulting in a net increase in synaptic strength in many brain circuits. Such increased synaptic weight would be unsustainable in the long run, due to increased demand for energy, space and supplies, and risk of synaptic saturation. Thus, according to the synaptic homeostasis hypothesis, sleep is important to renormalize synaptic strength to a baseline level that is sustainable and beneficial for memory and performance. There is strong evidence that the amplitude and slope of EEG slow waves is related to the number of neurons that enter an up state or a down state of the slow oscillation near-synchronously, and that synchrony is directly related to the number, strength, and efficacy of synaptic connections among them. Thus, the average synaptic strength (number or efficacy of synapses) reached in a given cortical area at the end of the major wake phase should be reflected by the level of SWA in the EEG at sleep onset. Moreover, according to the hypothesis, sleep SWA is not only a useful proxy of wake-related cortical synaptic strength, but could mediate the renormalization of neural circuits by favoring net synaptic depression, perhaps aided by low levels of norepinephrine, serotonin, and acetylcholine during NREM sleep. Here we briefly review human and animal studies showing that, consistent with this hypothesis, 1) in the adult cerebral cortex wake is associated with a net increase in synaptic strength, and sleep with a net decrease; and 2) SWA reflects not just prior “use” of specific neuronal circuits, but rather the occurrence of plastic changes, with increases in SWA after synaptic potentiation, and decreases in SWA after synaptic depression. We end by discussing current challenges to this hypothesis and future research directions.