Simultaneous Localization and Mapping (SLAM) involves creating an environmental map based on sensor data, while concurrently keeping track of the robot’s current position. Efficient and accurate SLAM is crucial for any mobile robot to perform robust navigation. It is also the keystone for higher-level tasks such as path planning and autonomous navigation. The past two decades have seen rapid and exciting progress in solving the SLAM problem together with many compelling implementations of SLAM methods. In this paper, we will review the two common families of SLAM algorithms: Kalman filter with its variations and particle filters. This article complements other surveys in this field by reviewing the representative algorithms and the state-of-the-art in each family. It clearly identifies the inherent relationship between the state estimation via the KF versus PF techniques, all of which are derivations of Bayes rule.