Degradation, damage evolution, and fatigue models in the literature for various engineering materials, mostly metals and composites, are reviewed. For empirical models established under the framework of Newtonian mechanics, Gurson–Tvergaard–Needleman (GTN) type model, Johnson-Cook (J-C) type damage model, microplasticity model, some other micro-mechanism based damage models, and models using irreversible entropy as a metric with an empirical evolution function are thoroughly discussed. For Physics-based models, the development and applications of unified mechanics theory is reviewed.