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This article surveys recent progress and discusses future opportunities for simultaneous localization and mapping (SLAM) in extreme underground environments. SLAM in subterranean environments, from tunnels, caves, and man-made underground structures on Earth, to lava tubes on Mars, is a key enabler for a range of applications, such as planetary exploration, search and rescue, disaster response, and automated mining, among others. SLAM in underground environments has recently received substantial attention, thanks to the DARPA Subterranean (SubT) Challenge, a global robotics competition aimed at assessing and pushing the state of the art in autonomous robotic exploration and mapping in complex underground environments. This article reports on the state of the art in underground SLAM by discussing different SLAM strategies and results across six teams that participated in the three-year-long SubT competition. In particular, the article has four main goals. First, we review the algorithms, architectures, and systems adopted by the teams; particular emphasis is put on light detection and ranging (LIDAR)-centric SLAM solutions (the go-to approach for virtually all teams in the competition), heterogeneous multirobot operation (including both aerial and ground robots), and real-world underground operation (from the presence of obscurants to the need to handle tight computational constraints). We do not shy away from discussing the “dirty details” behind the different SubT SLAM systems, which are often omitted from technical papers. Second, we discuss the maturity of the field by highlighting what is possible with the current SLAM systems and what we believe is within reach with some good systems engineering. Third, we outline what we believe are fundamental open problems, which are likely to require further research to break through. Finally, we provide a list of open-source SLAM implementations and datasets that have been produced during the SubT challenge and related efforts and constitute a useful resource for researchers and practitioners.