Abstract: In recent years, climate change has triggered increasingly frequent extreme precipitation events, thereby posing significant challenges to the safe operation of earth-rock dams. The scientific understanding and reasonable assessment of the overtopping-induced breaching process of earth-rock dams are crucial for disaster prevention and emergency response. The critical initiation conditions and quantitative characterization of earth-rock dam materials, the evolution mechanism of the breach morphology, and the numerical simulation of breach flood hydrograph are key research areas and challenges in the simulation of the overtopping-induced breaching process of earth-rock dams. Starting from the erosion characteristics of earth-rock dam materials, this paper systematically introduces the experimental equipment and testing methods for soil erosion characteristics, and summarizes the quantitative characterization methods for the critical shear stress and erosion rates of non-cohesive and cohesive dam materials. Based on dam breaching model experiments at different scales, the overtopping-induced breach morphology evolution mechanisms on homogeneous dams, core-wall dams, and concrete-faced rockfill dams are analyzed, and the instability patterns of breach side slopes and the failure mechanisms of dam impervious structures under water-soil coupling mechanism are revealed. From the perspectives of empirical analysis of peak breach flow, and the simplified and detailed analyses based on the overtopping-induced breaching mechanism, this paper elaborates on the numerical analysis methods for overtopping-induced breaching flood of earth-rock dams, and evaluates their applicability and solution methods. Although the theoretical and technical framework for simulating the overtopping-induced breach process of earth-rock dams has been initially established, there are still some difficulties to overcome, such as determination of the erosion parameters of dam materials under the uncertainties of materials and loads, accurate characterization of the breach development process, and efficient solution of the dam breaching flood using numerical methods. In the future, there will be a continued need for breakthroughs in multi-scale test equipment, high-precision testing techniques, and efficient numerical analysis methods to enhance the accuracy and practicality in the simulation of overtopping-induced breaching process of earth-rock dams.