Navigation is a fundamental problem of mobile robots, for which Deep Reinforcement Learning (DRL) has received significant attention because of its strong representation and experience learning abilities. There is a growing trend of applying DRL to mobile robot navigation. In this paper, we review DRL methods and DRL-based navigation frameworks. Then we systematically compare and analyze the relationship and differences between four typical application scenarios: local obstacle avoidance, indoor navigation, multi-robot navigation, and social navigation. Next, we describe the development of DRL-based navigation. Last, we discuss the challenges and some possible solutions regarding DRL-based navigation.