The dorsolateral and ventrolateral pons (dl-pons, vl-pons) are critical brainstem structures mediating the plasticity of the Hering-Breuer mechanoreflex (HBR) and carotid chemoreflex (CCR). Review of anatomical evidence indicates that dl-pons and vl-pons are connected reciprocally with one another and with medullary nucleus tractus solitarius (NTS) and ventral respiratory group (VRG). With this structural map, functional models of HBR and CCR are proposed in which the respiratory rhythm is modulated by short-term depression (STD) or potentiation (STP) of corresponding primary NTS-VRG and auxiliary pons-VRG excitatory or inhibitory pathways. Behaviorally, STD and STP of respiratory reflexes are akin to non-associative learning such as habituation, sensitization or desensitization to afferent inputs. Computationally, the STD and STP effects amount to signal differentiation and integration in the time domain, or high-pass and low-pass filtering in the frequency domain, respectively. These functional and structural models of pontomedullary signal processing provide a novel conceptual framework that unifies a wealth of experimental observations regarding mechanoreceptor and chemoreceptor reflex control of breathing.