Path planning is the most fundamental necessity for autonomous mobile robots. Traditionally, the path planning problem was solved using analytical methods, but these methods need perfect localization in the environment, a fully developed map to plan the path, and cannot deal with complex environments and emergencies. Recently, deep neural networks have been applied to solve this complex problem. This review paper discusses path-planning methods that use neural networks, including deep reinforcement learning, and its different types, such as model-free and model-based, Q-value function-based, policy-based, and actor-critic-based methods. Additionally, a dedicated section delves into the nuances and methods of robot interactions with pedestrians, exploring these dynamics in diverse environments such as sidewalks, road crossings, and indoor spaces, underscoring the importance of social compliance in robot navigation. In the end, the common challenges faced by these methods and applied solutions such as reward shaping, transfer learning, parallel simulations, etc. to optimize the solutions are discussed.