Current interest in the use of composites in many challenging applications of the naval and aeronautical industries, where the structural systems must withstand extreme loading conditions, highlights the need for a better understanding of the response of composite structures in the post-elastic regime, where different damage and failure mechanisms may form, evolve and interact controlling the mechanical response and final failure. Multiple delamination fracture at the layer interfaces is among the dominant failure mechanisms in laminated structures and is conveniently studied using a discrete layer approach, which describes the system as an assemblage of sub-layers joined by cohesive interfaces. Results obtained using this modeling approach in laminated and sandwich beams subjected to dynamic loading, which highlight the effects of damage progression on mechanical response and key properties, will be reviewed at the meeting. Then a novel approach to study delamination damage progression in laminated cylindrical shells subjected to dynamic loading will be presented. The proposed model uses a homogenization technique to reduce the number of displacement unknowns of the problem and is therefore expected to overcome the main drawback of classical discrete layer models.