Technical Abstract: A large number of embankment structures, including dams, levees, dikes, and barriers, have been built by humans. These structures play a very important role in flood defense, while many are also used for water supply, power generation, transportation, sediment retention, etc. Since these structures can sustain only limited safety levels and are subject to decay, they may fail due to various triggering mechanisms particularly with a high probability of failure under extreme conditions. Failure of these structures poses significant flood risks to people and property in the inundation area and cause interruption of services provided. Therefore, understanding and prediction of embankment failure processes are crucial for water infrastructure management. Great progress has been made recently to investigate embankment breaching processes through laboratory and field experiments and real-world case studies. A number of parametric simplified, and detailed multidimensional physically-based embankment breach models have been established in the past decades, but the prediction with these models involves significant uncertainties. The biggest limitation of the existing breach models is quantifying erosion rates or erodibility of cohesive soils and sediment entrainment under embankment break/breaching flows. A number of laboratory experiments and field investigations have been carried out and many empirical, analytical, and numerical models have been developed to first understand and then simulate the earthen embankment breaching processes. This paper provides an overview of the state of the art of several important related issues, including the earthen embankment breaching processes, data collection, breach modeling, flood routing, model limitations and uncertainties, and potential future development.