Intersection management is a sophisticated event in the intelligent transportation system due to a variety of behavior for traffic participants. This paper primarily overviews recent studies on the scenes of intersection, aiming at improving the efficiency or guaranteeing the safety when vehicles pass the crossing. These studies are respectively surveyed from the perspectives of efficiency and safety. Firstly, recent contributions to efficiency-oriented, intersection management overviews from four scenes, including congestion avoidance, green light optimized speed advisory (GLOSA), trajectory planning, and emergency vehicle priority preemption control. Furthermore, the studies on intersection collision detection and abnormal information warning are surveyed in the safety category. The corresponding algorithms for velocity and route management presented in the surveyed works are discussed.