1. The concept of dynamic materials (DM) as thermodynamically open formations in space-time. Cross-disciplinary implementations: properly material (mechanical or electromagnetic), biological (living tissue), environmental (traffic), etc. 2. Mathematical description: Minkowskian space-time. Tensor formulation of electrodynamics of moving bodies. Lorentz group, electrodynamic material tensor. Classification of DM into activated and kinetic. 3. Unusual effects: screening, light trapping, energy and power accumulation. 4. Activated materials: wave propagation across property interfaces in space-time. Regular and irregular reflection/transmission. Smooth and rugged property interfaces. 5. Homogenization of regular DM laminates. Coordinated wave propagation and screening. 6. A regular doubly periodic checkerboard DM in 1D-space + time. Energy and power accumulation along limit cycles. Limited energy supply. 7. Material geometry optimization in space-time. Relaxation through scaling and homogenization in a regular case, and through addition of special collision scenarios in irregular case. 8. Conclusions