More than 800,000 dams and thousands of kilometers of dikes have been constructed around the world. These structures are often designed based on a statistical analysis of the discharge distribution in rivers. However, the history of construction of dams and dikes coexists with the history of failures. Hundreds of dam failure events were reported worldwide in the previous century, while every year dikes breach due to high flows in the rivers or for other reasons leading sometimes to catastrophic consequences.In this book a description is presented of a framework and techniques for modelling structure failure events as well as a proposal to several novel approaches for risk analysis and assessment by numerical, statistical and constrained based methods in particular to the problems of breach modelling and flood water mitigation.