Embankment breaching processes are very complex and involve mixed-regime free-surface flow with overfalls and hydraulic jumps, pressurized pipe flow, strong vertical and lateral erosion, discrete mass failure, and headcut migration. The failure mode and mechanism are affected by upstream and downstream water conditions, embankment configurations, and soil properties and state. Great progress has been made to investigate embankment breaching processes through laboratory and field experiments and real-world case studies. However, most laboratory experiments were for smallscale homogeneous embankments, only a few outdoor experiments were conducted at large scales (up to several meters in height) and/or were of composite construction, and only limited data sets for historical embankment failures were sufficiently documented. A number of parametric, simplified physically-based, and detailed multidimensional physically-based embankment breach models have been established in the past decades, but 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. It is important to conduct more large-scale laboratory experiments and field case studies to improve existing embankment breach models or develop new ones. These models should also be enhanced by incorporating better physical insights, by using more efficient computational technologies, and integrating them into more robust flood forecasting and risk assessment systems with comprehensive relevant databases