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. This book gathers the presentation made during the Advanced Research Workshop held in Portoroz (Slovenia) in October 2008, under the auspices of NATO Science for Peace and Security Programme. It is edited by Professor Guy Pluvinage from the University Paul Verlaine – Metz (France) and Professor Aleksandar Sedmak from the University of Belgrade, Faculty of Mechanical Engineering. Both have a long and rich experience in analysis of theoretical and practical cases in safety and reliability of structures. Other contributors are all known as experts in the areas of fatigue, facture and reliability of structures.