The allocation of students to courses is a wide-spread and repeated task in higher education, often accomplished by a simple first-come first-served (FCFS) procedure. FCFS is neither stable nor strategy-proof, however. The Nobel Prize in Economic Sciences was awarded to Al Roth and Lloyd Shapley for their work on the theory of stable allocations. This theory was influential in many areas, but found surprisingly little application in course allocation as of yet. In this paper, different approaches for course allocation with a focus on appropriate stable matching mechanisms are surveyed. Two such mechanisms are discussed in more detail, the Gale-Shapley student optimal stable mechanism (SOSM) and the efficiency adjusted deferred acceptance mechanism (EADAM). EADAM can be seen as a fundamental recent contribution which recovers efficiency losses from SOSM at the expense of strategy-proofness. In addition to these two important mechanisms, a survey of recent extensions with respect to the assignment of schedules of courses rather than individual courses is provided. The survey of the theoretical literature is complemented with results of a field experiment, which help understand the benefits of stable matching mechanisms in course allocation applications. Copyright Springer Fachmedien Wiesbaden 2014
