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While sleeping, many vertebrate groups alternate between at least two sleep stages: rapid eye movement and slow wave sleep^{, , –}, in part characterized by wake-like and synchronous brain activity, respectively. Here we delineate neural and behavioural correlates of two stages of sleep in octopuses, marine invertebrates that evolutionarily diverged from vertebrates roughly 550 million years ago (ref. ) and have independently evolved large brains and behavioural sophistication. ‘Quiet’ sleep in octopuses is rhythmically interrupted by approximately 60-s bouts of pronounced body movements and rapid changes in skin patterning and texture. We show that these bouts are homeostatically regulated, rapidly reversible and come with increased arousal threshold, representing a distinct ‘active’ sleep stage. Computational analysis of active sleep skin patterning reveals diverse dynamics through a set of patterns …