The simultaneous localization and mapping (SLAM) algorithm is the key link in achieving the autonomous mobility of mobile robots. Light detection and ranging (LiDAR) has the advantages of high range accuracy, less susceptibility to external interference, and intuitive and convenient map construction, and is widely used in map construction for large and complex indoor and outdoor scenes. Domestic and foreign scholars have achieved fruitful results in the research of SLAM algorithms based on 3D LiDAR due to the application and popularity of 3D lasers. The current status of domestic and foreign research on 3D laser SLAM algorithms in front-end data association, back-end optimization, etc., and the principles and advantages and disadvantages of various 3D laser SLAM algorithms and improvement schemes are analyzed and summarized in combination with deep learning and multi-sensor fusion. The application of theories and technologies in 3D laser SLAM algorithms is described, and research hotspots and development trends of 3D laser SLAM algorithms are highlighted, including multi-source information fusion, integration with deep learning, the robustness of application scenarios, a generic framework for SLAM algorithms, and technology penetration of mobile sensors and wireless signal regimes. The research results have significant reference value and guiding significance for the research of 3D laser SLAM algorithms and instant localization and map construction of mobile robots in unknown environments.