Mobile robots are increasingly being applied in a variety of sectors, including agricultural, firefighting, and search and rescue operations. Robotics and autonomous technology research and development have played a major role in making this possible. Before a robot can reliably and effectively navigate a space without human aid, there are still several challenges to be addressed. When planning a path to its destination, the robot should be able to gather information from its surroundings and take the appropriate actions to avoid colliding with obstacles along the way. The following review analyses and compares 200 articles from two databases, Scopus and IEEE Xplore, and selects 60 articles as references from those articles. This evaluation focuses mostly on the accuracy of the different path-planning algorithms. Common collision-free path planning methodologies are examined in this paper, including classical or traditional and modern intelligence techniques, as well as both global and local approaches, in static and dynamic environments. Classical or traditional methods, such as Roadmaps (Visibility Graph and Voronoi Diagram), Potential Fields, and Cell Decomposition, and modern methodologies such as heuristic-based (Dijkstra Method, A* Algorithms, and D* Algorithms), metaheuristics algorithms (such as PSO, Bat Algorithm, ACO, and Genetic Algorithm), and neural systems such as fuzzy neural networks or fuzzy logic (FL) and Artificial Neural Networks (ANN) are described in this report. In this study, we outline the ideas, benefits, and downsides of modeling and path-searching technologies for a mobile robot.