Intersections are at the core of congestion in urban areas. After the end of the Second World War, the problem of intersection management has benefited from a growing body of advances to address the optimization of the traffic lights’ phase splits, timing, and offset. These contributions have significantly improved traffic safety and efficiency in urban areas. However, with the growth of transportation demand and motorization, traffic lights show their limits. At the end of the 1990s, the perspective of autonomous and connected driving systems motivated researchers to introduce a paradigm shift for controlling intersections. This new paradigm is well known today as autonomous intersection management (AIM). It harnesses the self-organization ability of future vehicles to provide more accurate control approaches that use the smallest available time window to reach unprecedented traffic performances. This is achieved by optimizing two main points of the interaction of connected and autonomous vehicles at intersections: the motion control of vehicles and the schedule of their accesses. Considering the great potential of AIM and the complexity of the problem, the proposed approaches are very different, starting from various assumptions. With the increasing popularity of AIM, this paper provides readers with a comprehensive vision of noticeable advances toward enhancing traffic efficiency. It shows that it is possible to tailor vehicles’ speed and schedule according to the traffic demand by using distributed particle swarm optimization. Moreover, it brings the most relevant contributions in the light of traffic engineering, where flow–speed diagrams are used to measure the impact of the proposed optimizations. Finally, this paper presents the current challenging issues to be addressed.