Localization forms the heart of various autonomous mobile robots. For efficient navigation, these robots need to adopt effective localization strategy. This paper, presents a comprehensive review on localization system, problems, principle and approaches for mobile robots. First, we classify the localization problems in to three categories based on the information of initial position of the robot. Next, we discuss on robot position update principles. Then, we discuss key techniques to localize the mobile robot such as: probabilistic approach, autonomous map building and radio frequency identification (RFID) based scheme. In the probabilistic localization section, we discuss the Markov localization and Kalman filter along with its extended versions. Autonomous map building focuses on the widely used simultaneous localization and mapping (SLAM) approach. This section also discusses on applying SLAM to localize brain-controlled mobile robots. Next, we discuss on applying evolutionary approaches to estimate optimal position. The RFID scheme addresses on effective utilization of RFID tags to track objects and position the robot. We then analyze on position and orientation errors occurred by different localization strategies. We conclude this paper by highlighting future research possibilities.