The definition of what sleep is depends on the method that is applied to record sleep. Behavioral and (electro)-physiological measures of sleep clearly overlap in mammals and birds , but it is often unclear how these two relate in other vertebrates and invertebrates. Homeostatic regulation of sleep, where the amount of sleep depends on the amount of previous waking, can be observed in physiology and behavior in all animals this was tested in. In mammals and birds, sleep is generally subdivided into two states, non-rapid eye movement (NREM) sleep and REM sleep. In mammals the combination of behavioral sleep and the changes in the slow-wave range of the NREM sleep electroencephalogram (EEG) can explain and predict the occurrence and depth of sleep in great detail. For REM sleep this is far less clear. Finally, the discovery that slow-waves in the NREM sleep EEG are influenced locally on the cortex depending on prior waking behavior is an interesting new development that asks for an adaptation of the concept of homeostatic regulation of sleep. Incorporating local sleep into models of sleep regulation is needed to obtain a comprehensive picture.