Apnoea and periodic breathing are the hallmarks of breathing for the infant who is born prematurely. Sustained respiration is obtained through modulation of respiratory-related neurons with inputs from the periphery. The peripheral arterial chemoreceptors, uniquely and reflexly change ventilation in response to changes in oxygen tension. The chemoreflex in response to hypoxia is hyperventilation, bradycardia and vasoconstriction. The fast response time of the peripheral arterial chemoreceptors to changes in oxygen and carbon dioxide tension increases the risk of more periodicity in the breathing pattern. As a result of baseline hypoxaemia, peripheral arterial chemoreceptors contribute more to baseline breathing in premature than in term infants. While premature infants may have an augmented chemoreflex, infants who develop bronchopulmonary dysplasia have a blunted chemoreflex at term gestation. The development of chemosensitivity of the peripheral arterial chemoreceptors and environmental factors that might cause maldevelopment of chemosensitivity with continued maturation are reviewed in an attempt to help explain the physiology of apnoea of prematurity and the increased incidence of sudden infant death syndrome (SIDS) in infants born prematurely and those who are exposed to tobacco smoke.