Path planning technology enables robots to plan safe and efficient travelling routes in various environments, in which path planning algorithms have a decisive impact on the robot’s navigation efficiency, ability to adapt to complex environments, and the effectiveness of goal achievement. The characteristics and application scenarios of mobile robot path planning algorithms can be divided into three categories: classical path planning algorithms, intelligent bionic path planning algorithms, and reinforcement learning-based path planning algorithms. This paper explores each type of algorithm’s benefits and drawbacks, as well as the application domains for each, and discusses the corresponding improvement strategies. It summarizes the key characteristics of the mentioned algorithms and elaborates in detail on their anticipated in-depth development directions; building on existing research, this paper looks forward to the future development trends of path planning algorithms for mobile robots.