A new theoretical approach is proposed for addressing the electrodynamics of heterogeneous media and structures, which takes into account the interrelation between physical phenomena on different length scales. Using volume averaging theory (VAT), parabolic partial differential equations containing integral or integro-differential terms are obtained for electromagnetic wave propagation in heterogeneous media. This theory allows one to accurately describe physical phenomena owing to its ability to take into account spatial scales, interfacial effects, the structural features of heterogeneous media such as high-T_c superconducting ceramics and absorbing composite materials, and heat and mass exchange in porous media. The approach is exemplified by analysis of functional structures with electrodynamic properties, in particular absorbing structures, and its conclusions are supported by experimental data. Issues pertaining to the anisotropy in the properties of composite materials and related functional structures are discussed.