It has still not been shown that current failure theories can be accurate for all loading configurations, boundary conditions, layups, and thicknesses of composite laminates. A comprehensive discussion is neither available in the most recent bibliographical reviews, nor in the most recent assessments of their accuracy. In this review article, new failure theories, recent improvements to existing theories, and the most relevant contributions to the modeling of failure mechanisms of composites with continuous reinforcement fibers are discussed, together with their recent applications. The most recent physically based practical failure criteria, which use standard engineering quantities, have affordable computational costs and do not require empirical parameters to be examined for a variety of situations. Their predictions are compared to those of generalized failure criteria currently implemented into widespread finite element codes. The objective is to offer designers a guidance of the range of validity of current theories. To enlarge the set of tests for a single theory, the sample test set, i.e., layups, constituent materials, loading configurations, and boundary conditions, and the experimental results used to develop a failure criterion are used for different criteria. The finite element analysis is carried out using three-dimensional (3D), mixed elements capable of very accurately predicting the local stresses. The ply level stresses are computed discretizing the layers by a 3D meshing. The fiber and matrix stresses, which can differ significantly from the ply level stresses, are computed using a local 3D discretization of the constituents. The phase-averaged fiber and matrix stresses and the ply level stresses are used for failure computations. It is seen that generalized failure criteria can be as accurate as physically based failure criteria for some cases, while the opposite occurs for other cases. Likewise, a criterion can be the most accurate for a particular case and inaccurate in other cases. None of the failure criteria considered appeared accurate for all of the cases considered. However, a group of physically based criteria is identified that, collectively, provides quite accurate predictions. These criteria could be used as reciprocal checks. There on 136 references cited in this reivew article.