Intelligent perception and automatic control in a complex unknown environment is one of the current research hotspots of robots in the field of control, and a new generation of artificial intelligence makes it possible to realize intelligent automation. In recent years, the new method of robot control using deep reinforcement learning in high-dimensional continuous state-action space has attracted the attention of relevant researchers. Firstly, the rise and development of deep reinforcement learning are first reviewed. The deep reinforcement learning algorithms for robot motion control are classified into two categories: value-based functions and policy gradients, and their typical algorithms and their related features are detailly described. Then, for the learning process before simulation to reality, five kinds of simulation platforms for robot motion control are briefly introduced, which are often used for deep reinforcement learning. Moreover, according to different types of research, the research progress of the deep reinforcement learning approach of robot motion control is expounded in five aspects, including autonomous navigation, object grasping, gait control, human-robot collaborative and multi-robot cooperation. Finally, the future challenges and development trends are summarized and anticipated.