This paper provides an overview of several key areas of operations research applications in the air transportation industry. Specific topics covered include the various stages of aircraft and crew schedule planning; revenue management, including overbooking and leg-based and network-based seat inventory management; and aviation infrastructure planning and operations (airports and air traffic management). In each of these cases, the paper provides both a historical perspective on OR contributions and a brief summary of cutting-edge technology. It also identifies some of the major research challenges for the future. The paper also addresses these factors by way of a Transportation Problem, Monte Carlo Simulation, and a Game Theory Matrix respectively. This study considers a multitude of factors paving the way for further research to consider solutions for problems of greater complexity.