Apnoea of prematurity (AOP) affects almost all infants born at <28 weeks gestation or with birth weight <1000 g. When untreated, AOP may be associated with negative outcomes. Because of these negative outcomes, effective treatment for AOP is an important part of optimising care of preterm infants. Standard treatment usually involves xanthine therapy and respiratory support. Cutting-edge work with stochastic vibrotactile stimulation and new pharmaceutical agents continues to expand therapeutic options. In this article, we review the pathophysiology of AOP, associated conditions and treatment options.