Numerous landslide dams have been induced in recent years as a result of frequent earthquakes and extreme climate hazards. Landslide dams present serious threats to lives and properties downstream due to potentially breaching floods from the impounded lakes. To investigate the factors influencing the stability of landslide dams, a large database has been established based on an in-depth investigation of 1,737 landslide dam cases. The effects of triggers, dam materials, and geomorphic characteristics of landslide dams on dam stability are comprehensively analyzed. Various evaluation indexes of landslide dam stability are assessed based on this database, and stability evaluation can be further improved by considering the dam materials. Stability analyses of aftershocks, surges, and artificial engineering measures on landslide dams are summarized. Overtopping and seepage failures are the most common failure modes of landslide dams. The failure processes and mechanisms of landslide dams caused by overtopping and seepage are reviewed from the perspective of model experiments and numerical analyses. Finally, the research gaps are highlighted, and pathways to achieve a more complete understanding of landslide dam stability are suggested. This comprehensive review of the recent advances in stability and failure mechanisms of landslide dams can serve as a key reference for stability prediction and emergency risk mitigation.