This book is an attempt to provide a uni?ed methodology to derive models for fatigue life. This includes S-N ?-N and crack propagation models. This is not a conventional book aimed at describing the fatigue fundamentals but rather a book in which the basic models of the three main fatigue approaches the stress-based the strain-based and the fracture mechanics approaches are contemplated from a novel and integrated point of view. On the other hand as an alternative to the preferential attention paid to deterministic models based on the physical phenomenological and empirical description of fatigue their probabilistic nature is emphasized in this book in which stochastic fatigue and crack growth models are presented. This book is the result of a long period of close collaborationbetween its two authors who although of di?erent backgrounds mathematical and mechanical both have a strong sense of engineering with respect to the fatigue problem. When the authors of this book ?rst approached the fatigue ?eld in 1982 (twenty six years ago) they found the following scenario: 1. Linear bilinear or trilinear models were frequently proposed by relevant laboratoriesandacademiccenterstoreproducetheW] ohler?eld. Thiswas the case of well known institutions which justi?ed these models based on clientrequirementsorpreferences. Thisledtotheinclusionofsuchmodels and methods as for example the up-and-down in standards and o?cial practical directives (ASTM Euronorm etc.) which have proved to be unfortunate.