Apnea of prematurity (AOP) affects the majority of infants born prematurely, before 34 weeks of gestational age. AOP is a common diagnosis in the neonatal intensive care unit and one of significant clinical importance, both immediate and long term, as it is associated with reduced survival and poorer respiratory and neurodevelopmental outcomes. In this review, we provide an up-to-date summary of recent advances in the understanding of the pathophysiology of AOP, as well as the clinical questions relevant to physicians and staff treating infants with AOP. Finally, we discuss monitoring and discharge decisions, as these are areas of significant uncertainty.