Autonomous navigation is an essential problem in robotics, and it has been applied in many indoor and outdoor applications, such as logistics, surveillance, agriculture, search and rescue, etc. However, the complexities of the environment make the navigation problem challenging. For example, for indoor scenarios, robots might need to navigate through dense crowds of people, and for outdoor environments, robots also need to adapt to different terrains and larger-scale scenarios. We investigate the challenges of navigation in both indoor and outdoor environments. My research focuses on the sub-problems of navigation, Motion Planning, Localization, and Trajectory Generation. For indoor and outdoor locomotion, we propose different Reinforcement learning-based models to handle different challenging environments, including dense crowds, bumpy or slippery terrains, different elevation changes, etc. Given a map and the locomotion method, a robot still needs to know its position for navigation. Therefore, for robot localization, we propose new models for indoor and outdoor place recognition with an RGBD camera or Lidar. For large-scale outdoor navigation, we investigate generative models for trajectory generation to cover all traversable areas. We deploy all our algorithms in real robots such as Turtlebot, Husky, and Spot robots in real-world environments.