Fundamentals of modern fracture mechanics are considered and the methods of their application: Griffith's theory, force and energy forms of critical state on front of a crack, the concept of stress intensity factor and three modes of stress state. Critical state conditions for ductile materials are analyzed: the J-integral as fracture criterion, critical crack opening displacement. Simplified form of dynamic crack propagation is considered. More details are examined on fatigue crack, corrosion-fatigue crack and corrosion critical stress intensity factor Kscc.