Infants who are born prematurely are at significant risk of apnoea. In addition to the short-term consequences such as hypoxia, apnoea of prematurity has been associated with long-term morbidity, including poor neurodevelopmental outcomes. Clinical trials have illustrated the importance of methylxanthine drugs, in particular caffeine, in reducing the risk of long term adverse neurodevelopmental outcomes. However, the extent to which apnoea is causative of this secondary neurodevelopmental delay or is just associated in a background of other sequelae of prematurity remains unclear. In this review, we first discuss the pathophysiology of apnoea of prematurity, previous studies investigating the relationship between apnoea and neurodevelopmental delay, and treatment of apnoea with caffeine therapy. We propose a need for better methods of measuring apnoea, along with improved understanding of the neonatal brain's response to consequent hypoxia. Only then can we start to disentangle the effects of apnoea on neurodevelopment in preterm infants. Moreover, by better identifying those infants who are at risk of apnoea, and neurodevelopmental delay, we can work toward a risk stratification system for these infants that is clinically actionable, for example, with doses of caffeine tailored to the individual. Optimising treatment of apnoea for individual infants will improve neonatal care and long-term outcomes for this population.