Research in this area concerns the often consistent, and sometimes competing, requirements on responses of materials for armor and anti-armor. For example, balances between high impedance and lightweight, strength and toughness, and material removal and energy absorbency place challenges on both the design of materials and the design of structures. In particular, microstructural design is important in the development of advanced materials for meeting specific performance objectives. Research in this area focuses on the characterization of structure-performance relations in ceramic and metallic composites. Combined computational and experimental methods are used, emphasizing an explicit account of microstructures, microstructural deformation, and failure processes. The computational analyses integrate deterministic tracking of fracture processes and stochastic quantification of the variability of material behavior. The experimental analyses emphasize digital high-speed photography and laser interferometry for the quantification of material response.