Floods caused by breaches of embankment and landslide dams are not only a tremendous geological disaster , destroying people's lives and property, they also strongly shape the appearance of the landscape in the inundation area. This review addresses embankment and landslide dam breaches, with a particular focus on documented failure cases, laboratory and field experiments, as well as empirically and physically based models. The state of the art of physical and mathematical modeling technologies of underlying breach mechanisms and processes are also reviewed. First, the distribution, breach parameters, and failure modes of documented failure cases are analyzed. Second, based on physical model tests at different scales around the world, the breach processes of embankment and landslide dams caused by overtopping or piping/seepage are studied in depth. The breach characteristics for each type of dam are summarized. Third, typical empirically or physically based mathematical models are reviewed with a focus on artificially formed dams (i.e., earthfill, clay core rockfill , and concrete face rockfill dams) or naturally formed dams (i.e., landslide dams). Both uncertainties and limitations associated with formulations and calculating parameters of these mathematical models are also discussed. Finally, recommendations toward a better understanding of breach mechanisms and further development of mathematical models are proposed.