The terrain aided navigation system relies on terrain elevation features as the source of positioning information, providing bounded positioning errors for underwater vehicles. Substantial suppression of error drift in strapdown inertial navigation systems is achieved. The terrain matching algorithm is the key technology of terrain aided navigation system, and its output matching position can be used as the observation value of the integrated navigation filter to correct the navigation parameters. The accuracy of terrain matching directly determines the performance of the whole navigation system. An overview of existing underwater navigation and positioning technologies was presented. Subsequently, the fundamental principles and components of terrain aided navigation were expounded. Finally, a detailed summary was provided regarding the domestic and international research progress on terrain aided navigation systems and terrain matching algorithms. This offers beneficial reference and support for the development and research of terrain aided navigation systems in our country.