Sleep has been classically described as an all-or-nothing global phenomenon. However, recent research strongly suggests that this view requires tempering. Invasive and non-invasive recordings in animals and humans show that neural activity typically associated with sleep can locally occur during wakefulness. Although local sleep is defined neuronally, it has been associated with impaired performance during cognitive tasks. Comparatively, the phenomenology of local sleep (i.e., what it feels like when your brain is partially asleep) has been less explored. Taking into account the literature on the neuronal and behavioral profile of local sleep intrusions in wakefulness, we propose that occurrences of local sleep could represent the neural mechanism underlying many attentional lapses. In particular, we argue that a unique physiological event such as local sleep could account for a diversity of behavioral outcomes from sluggish to impulsive responses. We further propose that local sleep intrusions could impact individuals’ subjective experience. Specifically, we propose that the timing and anatomical sources of local sleep intrusions could be responsible for both the behavioral consequences and subjective content of attentional lapses and may underlie the difference between subjective experiences such as mind wandering and mind blanking. Our framework aims to build a parallel between spontaneous experiences in sleep and wakefulness by integrating evidence across neuronal, behavioral and experiential levels. We use the example of attention deficit hyperactivity disorder (ADHD) to illustrate how local sleep could explain complex cognitive profiles which include inattention, impulsivity, mind-wandering and mind-blanking.