Landslide dams constitute significant geological hazards, accompanied by challenges such as limited field data, urgent response requirements, and difficult mitigation conditions. This review systematically examines the topographic, hydrological, and geotechnical factors influencing dam formation and stability, highlighting the critical roles of material composition and internal structure in breach development. Existing methodologies for modeling dam-break scenarios, including statistical, parametric, simplified physically-based, and refined physically-based models, are critically evaluated, revealing persistent challenges such as parameter uncertainty, scale effects in physical experiments, and scarcity of field validation data. In addition, both engineering and non-engineering strategies for emergency response are reviewed. Key research gaps include an insufficient understanding of multi-phase interactions during dam failure, the potential for engineering interventions to alter failure modes (e.g., from overtopping to piping), the need for an improved dynamic risk assessment framework, and the integration of real-time data assimilation technologies. Finally, this review proposes future directions, including enhanced multi-source monitoring, machine learning-aided parameter inversion, uncertainty quantification and probabilistic forecasting, and improved dam-break models, to support effective decision-making in emergency scenarios.