Given a set of scheduled flights that must be operated by the same aircraft type, the aircraft routing problem (ARP) consists of building anonymous aircraft routes that respect maintenance requirements and cover each flight exactly once. This paper surveys the literature on this problem and introduces a classification according to three business processes that are used to assign the anonymous routes to the specific aircraft tail numbers. Furthermore, we compare the ARP variants resulting from these three processes with regard to their adaptability to different contexts, the difficulty of solving them, the cost of the computed solutions, and the robustness of these solutions.