Autonomous Underwater Vehicles (AUVs) have been used for a huge number of tasks ranging from commercial, military and research areas etc, while the fundamental function of a successful AUV is its localization and mapping ability. This report aims to review the relevant elements of localization and mapping for AUVs. First, a brief introduction of the concept and the historical development of AUVs is given; then a relatively detailed description of the sensor system used for AUV navigation is provided. As the main part of the report, a comprehensive investigation of the simultaneous localization and mapping (SLAM) for AUVs are conducted, including its application examples. Finally a brief conclusion is summarized
