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The normal operation of aircraft and flights can be affected by various unpredictable factors, such as severe weather, airport closure, and corrective maintenance, leading to disruption of the planned schedule. When a disruption occurs, the airline operation control center performs various operations to reassign resources (e.g., flights, aircraft, and crews) and redistribute passengers to restore the schedule while minimizing costs. We introduce different sources of disruption and corresponding operations. Then, basic models and recently proposed extensions for aircraft recovery, crew recovery, and integrated recovery are reviewed, with the aim of providing models and methods for different disruption scenarios in the practical implementation of airlines. In addition, we provide suggestions for future research directions in these topics.