This article presents a review of the progressive failure theories for analysing composites by using computational analysis methods like finite element method. Failure severity can be represented by the degree to which the elastic properties of a ply are damaged. Fibre failure is usually assumed to cause the failure of the matrix. So these fibre ply-to-ply failure mechanisms will be studied and analysed for better usage of the models for respective analysis. Sudden degradation models study the ply loading history with increase in loading, elastic properties will be reduced by a discrete factor resulting to successive failure mechanisms. Such models and failure mechanisms were studied and a detailed review was presented with possible simulation models in progressive failure of composites.