Recent developments in the aircraft industry towards substantially improving fuel economy and extending flight range have accelerated interest in the use of advanced composites as primary structural materials. The airframes of next-generation airliners will have substantial parts made of light-weight composites. This means that the engineering demands on the performance of fiber-reinforced composites will become greater. There is therefore a need to better understand and predict the multiple complex failure mechanisms in composite structures, and to devise more reliable failure theories and damage progression models. There is a large body of literature on progressive damage analysis in composites, much of which employs damage mechanics and material stiffness degradation methods. This article reviews some of the more recent work in this area and describes the issues pertinent to application in composite structures. The authors' ongoing research efforts in modeling and prediction of progressive damage through the relatively novel element-failure method (EFM), which has been coded into a user-defined UEL code in Abaqus, are discussed. In particular, results for notched composite laminates and pin-loaded (PL) analyses are shown and compared to experimental data. Although EFM is the computational platform on which the damage is advanced in the structure, the results are dependent on the choice of the failure criterion. Various failure criteria are used throughout the cases discussed herein, from the more traditional Tsai—Wu (TW) criterion to the very recently proposed micromechanics-based failure (MMF) criterion. The EFM may also be used with cohesive elements, with the former intended for modeling in-plane damage progression, while the latter for delamination onset and propagation. This hybrid EFM-cohesive element approach is illustrated with an analysis of double-notched composite laminate. The computational models are relatively robust up to and including ultimate load, and enable the mapping of extensive damage patterns in composite structures. They represent a suite of computational tools that extend the capability to model damage and failure propagation beyond initial failure prediction.