In this paper we provide a wide-ranging review of the literature on stochastic modeling applications within aviation, with a particular focus on problems involving demand and capacity management and the mitigation of air traffic congestion. From an operations research perspective, the main techniques of interest include analytical queueing theory, stochastic optimal control, robust optimization and stochastic integer programming. Applications of these techniques include the prediction of operational delays at airports, pre-tactical control of aircraft departure times, dynamic control and allocation of scarce airport resources and various others. We provide a critical review of recent developments in the literature and identify promising research opportunities for stochastic modelers within air traffic management.