In this paper an overview of the research activities related to an approach that has been developed independent of stress intensity factors and fracture toughness parameters is presented for the computational simulation of progressive fracture in polymer-matrix composite structures. The damage stages are quantified based on physics via composite mechanics while the degradation of the structural behavior is quantified via the finite element method. The approach accounts for all types of composite behavior, structures, load conditions, and fracture processes starting from damage initiation, to unstable propagation and to global structure collapse. Results of structural fracture in composite plates, shells and built-up structures are presented to demonstrate the effectiveness and versatility of this approach. Parameters/guidelines are identified that can be used as criteria for structural fracture, inspection intervals, and retirement for cause. Generalization to structures made of any or combinations of materials are outlined, and lessons learned in undertaking the development of computational simulation approaches, in general, are summarized.