Neuronal activities that synchronize with the breathing rhythm have been found in humans and a host of mammalian species, not only in brain areas closely related to respiratory control or olfactory coding but also in areas linked to emotional and higher cognitive functions. In parallel, evidence is mounting for modulations of perception and action by the breathing cycle. In this Review, we discuss the extent to which brain activity locks to breathing across areas, levels of organization and brain states, and the physiological origins of this global synchrony. We describe how waves of sensory activity evoked by nasal airflow spread through brain circuits, synchronizing neuronal populations to the breathing cycle and modulating faster oscillations, cell assembly formation and cross-area communication, thereby providing a mechanistic link from breathing to neural coding, emotion and cognition. We argue that, through evolution, the breathing rhythm has come to shape network functions across species.