Structures that are essential for economy and security such as energy production, transportation and supply, water supply, buildings, are susceptible to failure, because of defects already present in the material, or created at fabrication, or appearing during service. Methods of assesment of the nocivity of these defects are needed, to predict the remaining service life and the eventual emergency of stopping service and repairing, if possible. To reach this objectives, this book presents the last methods derived from the classical linear, non-linear fracture mechanics concepts, including fatigue and notch fracture mechanics. Several examples of structures rehabilitations and repairing are given.