In recent years, recurrent floods have been observed in many countries around the world that may have led to overtopping dams, resulting in dam breaches and catastrophic floods on the downstream of these structures. This leads to various damages such as loss of social wealth, large-scaled economical expenses, and the loss of lives. Therefore, reviewing and understanding the cause of embankment dams overtopping, behaviors of dams while overtopped and suggestion of possible solution is of tremendous significance for dam failure damage assessment, disaster control, risk analysis and mitigation, etc. In this review paper, a number of factors that influence embankment dam overtopping were identified and discussed, and the areas that require further studies were also recognized. Meanwhile, by considering types of construction materials, the characteristics and the appearances of embankment dam breaching during overtopping and mitigation measure discussed, the importance of breach models were described and summarized. Finally, recommendations and proposed future studies were made on traditional design approaches, breach characteristics for composite dams, breach modeling, the position for breach initiation and statistical analysis for dams at the end of service life.