Background: Path-planning algorithms are widely used in robotics, vehicles, UAVs, carrier-based aircraft towing vehicles, etc. Using these algorithms, an optimal path with safe obstacle avoidance and high efficiency can be planned. In recent years, path-planning algorithms have received more and more attention from scholars at home and abroad. Objective: In order to promote the application and development of path-planning algorithms, an in-depth analysis of the current development status of path-planning algorithms was presented. The most widely used and representative algorithms in several representative results were extracted, and the characteristics and advantages and disadvantages of each algorithm were analyzed and elaborated in detail for the readers' reference. Methods: The existing path-planning algorithms were classified, and a brief overview of each traditional algorithm was given, followed by an in-depth study of the improved algorithms to summarize the advantages and disadvantages of each type of algorithm. Finally, based on these research results, the future development trend of path-planning algorithms was projected. Results: Through the research and analysis of the path-planning algorithm, it was found that the path- planning algorithm before the improvement had the problems of an unsmooth path, low computational efficiency, a slow response time, the inability to safely avoid obstacles, etc. After the improvement and optimization of the path-planning algorithm, the performance was greatly improved. Conclusion: After research and analysis, it was found that multi-algorithm fusion had great potential for development in path-planning compared to the application and optimization of a single algorithm. In addition, further research is needed in the areas of algorithm adaptability, fusion, intelligent algorithms, and extending the range of algorithmic applications.