The prerequisite for underwater vehicles to accomplish various underwater tasks is to obtain real-time position information about themselves in the underwater environment using internal or external sensors, which is known as underwater positioning and navigation technology. This paper presents a general review of underwater vehicle positioning and navigation technology and illustrates the importance of underwater terrain-aided navigation technology. It also summarizes its general structure and describes the principles and functions of each component. The paper mainly analyzes various mainstream methods applied to underwater terrain-aided navigation, focuses on terrain suitability analysis and terrain matching algorithms, which play a central role in the analysis. Additionally, the research progress of terrain-aided navigation technology is described, and the research methods of terrain suitability analysis, terrain matching navigation, and the latest technology applications are compared. Some shortcomings of the current underwater terrain-aided navigation technology are presented, and future research directions are foreseen to provide a basis for subsequent research.