As an important branch of mobile robots, quadruped robots have high flexibility, high adaptability, and high dynamics, which provide excellent maneuverability and environmental adaptability. In the past ten years, researchers have done a lot of research on the ability of the quadruped robot to cope with the complex environment and published many results in order to make the working environment of the quadruped robot closer to reality. This paper collected these research results and divided these literatures into three categories according to different situations: crossing challenging terrain, walking on slope, and coping with interference, respectively, introducing representative methods. The purpose of this review is to summarize and analyze the previous research results and provide guidance for future research on quadruped robots in complex situations.