Heterogeneous functional materials, e.g., “HeteroFoaMs” are at the heart of countless energy systems, including heat storage materials, batteries, solid oxide fuel cells, and polymer electrolyte fuel cells. HeteroFoaMs are generally nanostructured and porous to accommodate transport of gasses or fluids, and must be multifunctional (i.e., active operators on mass, momentum, energy, or charge, in combinations). This paper will discuss several aspects of modeling the relationships between the constituents and microstructure of these material systems and their device functionalities. Technical advances based on these relationships will also be identified and discussed. Three major elements of the general problem of how to model HeteroFoaM electrodes will be addressed. Modeling approaches for ionic charge transfer with electrochemistry in the nanostructured porosity of the electrode will be discussed. Second, the effect of morphology and space charge on conduction through porous doped ceria particle assemblies, and their role in electrode processes will be modeled and described. And third, the effect of local heterogeneity and morphology on charge distributions and polarization in porous dielectric electrode materials will be analyzed using multiphysics field equations set on the details of local morphology. Several new analysis methods and results, as well as experimental data relating to these approaches will be presented. The value, capabilities, and limitations of the approaches will be evaluated.