The success of any progressive failure analysis of composite structures is influenced by the failure criteria and the associated material property degradation models. The failure criteria are the conditions for the prediction of the occurrence of material damage. The degradation models are mathematical representations of the residual properties for each material damage state predicted by the failure criteria. A brief summary of the major classes of failure criteria pertaining to the degradation models is followed by a review of degradation models that have been developed for unidirectional polymer matrix composite laminates. The review is organized around the relationships of the various models to associated failure criteria as well as the various constitutive frameworks for finite element implementation. Models that invoke residual properties as a one-time sudden degradation of the original properties are described followed by models where the mathematical representation of at least one property invokes gradual property degradation as a function of some other evolving field variable.