Computer-aided Air Traffic Management has increasingly attracted the interest of Operations Research community. This includes, among other tasks, decision support tools for detection and resolution of conflict situations on flight. Even if numerous optimization approaches have been proposed, there has been little debate towards homogenization. We synthesize the efforts made by the Operations Research community in the past few decades to provide mathematical models to aid conflict detection and resolution. Different mathematical representations of aircraft separation conditions are presented under a unified framework. The models, which hinge on these conditions, are then revisited, providing insight into their computational performance.