Simultaneous localization and mapping technology is the basis for multi-robot systems to complete navigation, path planning, and autonomous exploration in complex, dynamic, and Global Positioning System (GPS)-denied environments. This paper reviews the current status and progress of multi-robot simultaneous localization and mapping (SLAM) technology based on LiDAR. First, this paper studies the basic principles of LiDAR SLAM. It analyzes the system model construction of LiDAR SLAM, including the mobile robot coordinate system model, kinematic model, sensor model, map presentation, LiDAR SLAM framework, and classic algorithms. Then, this paper discusses the basic framework of collaborative SLAM, analyzes the key issues such as data association, loop closure detection, and global graph optimization in collaborative SLAM, and conducts a detailed literature review on the solutions to key problems in sub-fields of multi-robot SLAM such as frontier detection, task allocation, map fusion, and compares the advantages and disadvantages of various algorithms. Finally, this paper outlines the challenges and future research directions of multi-robot LiDAR SLAM.