Cortical oscillations in the range of alpha activity (8-13 Hz) are one of the fundamental electrophysiological phenomena of the human electroencephalogram (EEG). Evidence from quantitative EEG data has shown that their electrophysiological features, cortical generation mechanisms, and therefore, their functional correlates vary along the sleep-wake continuum. Specifically, spectral microstructure and EEG coherence levels between anterior and posterior cortical regions permit to differentiate among alpha activity spontaneously appearing in relaxed wakefulness with eyes closed, drowsiness period, and REM sleep, by reflecting distinct properties of neural networks involved in its cortical generation as well as a different interplay between cortical generators, respectively. Besides, the dissimilar spatiotemporal features of brain electrical microstates within the alpha range reveals a different geometry of active neural structures underlying each alpha variant or, simply, changes in the stability level of neural networks during each brain state. Studies reviewed in this paper support the hypothesis that two different alpha variants occur during human REM sleep: 'background responsive alpha activity', blocked over occipital regions when rapid eye movements are present, and 'REM-alpha bursts', non modulated by the alteration of tonic and phasic periods. Altogether, evidence suggests that electrophysiological features of human cortical oscillations in the alpha frequency range vary across different behavioural states, as well as within state, reflecting different cerebral phenomena with probably dissimilar functional meaning.