P lagued by high labor costs, low profitability margins, airspace and airport congestion, high capital and operating costs, security and safety concerns, and complex and large-scale management and operations decisions, the airline industry has armed its planners with sophisticated optimization tools to improve decision making and increase airline profits. In this paper, we describe optimization approaches for airline schedule planning, demonstrating how optimization can facilitate the management of a diverse and finite set of expensive, highly constrained resources. We focus on the art and science of modeling and solving these problems, providing illustrative examples of the associated impacts and challenges, and highlighting effective techniques that might be applicable to problems arising in other industries.