At present, path-planning for mobile robots is a hot problem. In the previous scientific research, A*, Dijkstra, rapidly-exploring random tree (RRT) and many other algorithms have appeared. To provide a clearer understanding of these algorithms, this article organized the idea and development of Q-learning, A* algorithm, ant colony algorithm, RRT algorithm and Dijkstra algorithm. According to the time order, this article researched several applications of the five algorithms respectively. Besides, optimization of the five algorithms in the past few years were listed. There are also examples of combined algorithms, which have better efficiency compared to using one algorithm alone. By analyzing the five algorithm and their optimization, the common problem and solution was found. The common problem of these algorithms is that a shorter and smoother path needs to be solved and the convergence speed needs accelerating. At present, the main solution can be divided into two aspects. One is to improve the algorithm itself, and the other is to combine different algorithms. In the future, more kinds of combined algorithms will emerge, and a better solution of path planning can be obtained to improve efficiency and reduce energy cost.