In this paper we consider the modelling and optimal control of queues of aircraft waiting to use the runway(s) at airports, and present a review of the related literature. We discuss the formulation of aircraft queues as nonstationary queueing systems and examine the common assumptions made in the literature regarding the random distributions for inter-arrival and service times. These depend on various operational factors, including the expected level of precision in meeting pre-scheduled operation times and the inherent uncertainty in airport capacity due to weather and wind variations. We also discuss strategic and tactical methods for managing congestion at airports, including the use of slot controls, ground holding programs, runway configuration changes and aircraft sequencing policies.