Knowledge about the own pose is key for all mobile robot applications. Thus pose estimation is part of the core functionalities of mobile robots. In the last two decades, LiDAR scanners have become a standard sensor for robot localization and mapping. This article surveys recent progress and advances in LiDAR-based global localization. We start with the problem formulation and explore the application scope. We then present the methodology review covering various global localization topics, such as maps, descriptor extraction, and consistency checks. The contents are organized under three themes. The first is the combination of global place retrieval and local pose estimation. Then the second theme is upgrading single-shot measurement to sequential ones for sequential global localization. The third theme is extending single-robot global localization to cross-robot localization on multi-robot systems. We end this survey with a discussion of open challenges and promising directions on global lidar localization.