This paper presents recent advances in our understanding of how structure (at all scale levels) influences and in many cases controls selected properties and performance of heterogeneous functional materials (HeteroFoaMs). We begin with mesomorphology and surface/volume discussions, and conclude with methods and concepts that start at the atomic level. Special attention is given not only to equilibrium processes but also to nonequilibrium behavior that controls, for example, the confinement of nuclear waste products. Surface to volume transitions and other principles are identified. The paper is written in outline form, with the purpose of identifying principles for further study. The significance of the findings is illustrated with discussions of applications to composite structures, nuclear fuel storage materials, functional materials used in electronics, oxide thin films, and batteries.