The objective of this thesis was to review and analyze existing algorithms for robot localization and mapping in dynamic indoor environments. Some of the existing algorithms include occupancy grid approach, artificial intelligence approach, dense scene flow approach for localization and mapping in dynamic environments. The occupancy grid approach maintains static and dynamic occupancy grids in parallel. The artificial intelligence approach uses efficient path planning algorithms like Reinforcement Learning along with Simultaneous Localization and Mapping (SLAM) to find a path and map the unknown dynamic environment. The dense scene flow approach detects moving objects to improve the visual SLAM process.The review phase of this work included identifying different approaches and classifying them. The classification of the different approaches was based on sensors used (in the data acquisition process), localization method used, and map management techniques used. These approaches were categorized into fixed sets. The review of these algorithms lead to a comparison of the already obtained results of these algorithms.The analysis phase of this work included implementing path planning algorithms on TurtleBot2 with real-time obstacle detection and avoidance. The results obtained were evaluated in terms of a set of fixed parameters. These parameters were accuracy of the algorithm, total time for execution, and errors in planning the final path for the robot.