Sleep is classically presented as an all-or-nothing phenomenon. Yet, there is increasing evidence showing that sleep and wakefulness can actually intermingle and that wake-like and sleep-like activity can be observed concomitantly in different brain regions. I will here explore the implications of this conception of sleep as a local phenomenon for cognition and consciousness. In the first part of my presentation, I will show how local modulations of sleep depth during sleep could support the processing of sensory information by sleepers. I will also how, under certain circumstances, sleepers can learn while sleeping but also how they can forget. In the second part, I will show how the reverse phenomenon, sleep intrusions during waking, can explain modulations of attention. I will focus in particular on modulations of subjective experience and how the local sleep framework can inform our understanding of everyday phenomena such as mind wandering and mind blanking. Through this presentation and the exploration of both sleep and wakefulness, I will seek to connect changes in neurophysiology with changes in behaviour and subjective experience.