Sleep suppresses the ability to react to environmental demands. It has been proposed that a phenomenon of sensory isolation, whereby sensory inputs fail to reach cortical brain regions during sleep, would be responsible for this absence of responses. How and why this decoupling is implemented has been intensively investigated. However, sleepers might not be fully disconnected from their environment. We review here the empirical evidence showing that sleepers can perform a surprisingly large range of cognitive processes. We describe potential mechanisms explaining sleepers’ ability to maintain covert cognitive processes as well as their suppression. Rather than being isolated from the environment, sleepers seem to enter a standby mode, allowing them to balance the monitoring of their surroundings with sensory isolation. This balance could allow sleepers to determine when to stay asleep or when to wake up, and might be essential for the fulfilment of sleep functions, notably memory consolidation.