Path planning, crucial in robotics and autonomous vehicles, involves finding efficient routes from start to finish while avoiding obstacles. Graph search algorithms like BFS, DFS, and A* are commonly used for this purpose. This research focuses on analyzing these algorithms' performance and applicability in diverse scenarios. The study provides a comprehensive overview of path planning's definition, application domains, and fundamental principles. It then delves into the core graph search algorithms: BFS explores nodes layer by layer, ensuring the shortest path is found first but suffering from high time complexity. DFS explores nodes in a depth-first manner, potentially leading to shorter paths but risking getting trapped in local optima. In contrast, A* combines the strengths of BFS and DFS by using heuristic functions to guide the search for the cheapest path to the goal. Despite their utility, graph search algorithms have limitations. The high time complexity of A* in large-scale environments and the potential for local optima are key challenges. To address these, research explores improved methods like GBFS and bidirectional A* search. The future direction of research includes developing more efficient heuristic functions, exploring hybrid algorithms, parallelizing path planning, and applying these methods to new domains like autonomous drones and self-driving cars. This research paves the way for more robust and efficient path planning algorithms in various applications.