of its most significant contributions to date. Examples of important topics that are either not covered at all or are touched on peripherally include: aviation safety and security, airline fleet planning, airline staffing, airline maintenance planning, aircraft loading, and decision support tools for the management of airport operations (e.g., gate assignments). Moreover, the specific topics and contributions that are highlighted are presented in nonquantitative terms and largely reflect the authors’ own interests. In addition to the bibliographic references associated with these contributions, other survey papers, which provide additional details and references, are cited whenever possible. Section 2 of the paper deals with the classical problems of scheduling, routing, and crew assignment in the airline industry. This is a context that is perfectly suited to the use of large-scale, discrete optimization approaches and, indeed, has motivated several methodological and computational developments in this vibrant area of OR over the years. Section 3 covers airline revenue management, including overbooking, flight leg yield management and network revenue maximization. Through a combination of stochastic and optimization models, OR work in this area has generated significant additional revenues for the airlines ever since the late 1980s. Moreover, revenue management continues to be a field in which airlines are vying intensively for competitive advantage. Section 4 surveys selected applications of OR to the study, planning, and design of the two major pieces of aviation infrastructure, the airports system and the air traffic management (ATM) system. Historically the emphasis here has been on stochastic models, as the questions addressed have focused on capacity, delays, and safety under conditions in which the probabilistic characteristics of the input parameters play a dominant role. However, optimization models, both deterministic and stochastic, have found use in the intensive recent research on air traffic flow management, a topic also reviewed briefly in §4. Finally, §5 summarizes the main conclusions regarding the fundamental challenges faced by future research.