From Leonardo da Vinci and Galileo Galilei, with the very first studies on strength of materials, to Allan Griffith, Charles Inglis, and George Irwin, with the pioneering studies on fracture mechanics, it is addressed the failure of structures using examples from the naval, aeronautical, and nuclear industries. It is presented a short history of fracture mechanics, with the focus of its application for the main (pressurized) components in the nuclear industry, and briefly introduced the concepts of brittle and ductile fractures, and the crack growth due to fatigue and stress corrosion cracking. The theory behind these is detailed in the chapters of the first part and applied in the case examples along the second part of the book, some of them using actual problems in the Brazilian nuclear plants.