The airline crew scheduling problem has received extensive attention, particularly in the last sixty years. This problem is frequently divided into crew pairing and crew assignment because of its large size and the complex safety agreements and contractual rules. Several solution methodologies have been developed, but many objectives and constraints are treated approximately and research is ongoing. In this paper, we present a comprehensive problem definition for the airline crew scheduling problem, and we review existing problem formulations and solution methodologies. In addition, we formulate the personalized cockpit crew scheduling problem as a set covering problem and we solve it using column generation. We present computational results for real data from a major US carrier, and we describe the data sets (available on the internet) in detail to establish a basis for future research.