Respiratory rhythms sustain biological life, governing the homeostatic exchange of oxygen and carbon dioxide. Until recently, however, the influence of breathing on the brain has largely been overlooked. Yet new evidence demonstrates that the act of breathing exerts a substantive, rhythmic influence on perception, emotion, and cognition, largely through the direct modulation of neural oscillations. Here, we synthesize these findings to motivate a new predictive coding model of respiratory brain coupling, in which breathing rhythmically modulates both local and global neural (...) gain, to optimize cognitive and affective processing. Our model further explains how respiratory rhythms interact with the topology of the functional connectome, and we highlight key implications for the computational psychiatry of disordered respiratory and interoceptive inference. (shrink)