Over the years, researchers in the River Research Department of the Changjiang River Scientific Research Institute has conducted extensive studies on the mechanism, models, and simulation technologies of embankment breaches due to overflowing. These efforts were aimed at enhancing the ability to respond to embankment breach emergencies and to defend associated disasters. Through the use of physical model tests, flume tests, theoretical analysis, numerical simulation, and other methods, the department has made significant contributions to the field. Specifically, we have uncovered the mechanism of embankment breaches due to overflowing, analyzed the role of “headcut erosion” in the breaching process, and introduced patterns of headcut erosion and phases of embankment breaching due to overflowing. Additionally, we have developed a two-dimensional mathematical model of headcut erosion and a mathematical model of embankment breaching based on the physical mechanism. Furthermore, we have created one-, two-, and three-dimensional flood simulation technologies that are adapted to the characteristics of dam-breaking flow, along with a terrain processing method, and have preliminarily explored the three-dimensional flow field and hydrodynamic pressure characteristics of dam-breaking flow. Last, we made a review on the research progress in related fields and the achievements published in scientific journals. The accomplishments of the department have already proven to be highly effective in emergency response and decision-making, specifically during the Tangjiashan and Baige barrier lake breach emergencies. These achievements provide technical reference and experience for addressing embankment breach (including barrier lake burst) dangers in the future.