Abstract The term ‘sleep debt’ is widely used to describe the effects of sleep loss. The construct of sleep debt, however, is poorly defined in the scientific literature. Cumulative build-up of sleep pressure appears to be a key feature of sleep debt. The concepts of ‘core sleep’ and ‘basal sleep need’ have been proposed to provide a theoretical framework, albeit without strong empirical basis. It has been hypothesized that adaptation to sleep debt may be possible over time, but experimental evidence for this hypothesis is ambiguous. Recent experiments using chronic sleep restriction have revealed significant effects of sleep debt on daytime sleep latency and behavioral alertness. In a series of strictly controlled laboratory studies, we found that sleep debt can lead to fundamentally different daytime responses, depending on whether homeostatic sleep pressure (as measured in the waking electroencephalogram (EEG)) or behavioral alertness (as measured with psychomotor vigilance lapses) is considered. This suggests the existence of an as yet unidentified regulatory mechanism of waking neurobehavioral function. To study the nature of this regulatory process under chronic sleep restriction, advantage can be taken of the natural variability in sleep need frequently cited in the literature. We also obtained evidence for interindividual differences in vulnerability to sleep loss regardless of sleep need. Statistical modeling of the effects of chronic sleep restriction on behavioral alertness, taking into account these interindividual differences, provided a reference for defining sleep debt. The results suggested that sleep debt may be defined as the cumulative hours of sleep loss with respect to a subject-specific daily need for sleep.