Many of the advanced composite materials used in aerospace, energy storage and conversion, and electrical devices are multifunctional, i.e., they operate on (or in the presence of) some combination of mechanical, thermal, electrical, chemical, and magnetic fields. Designing composite materials for airplanes, for example, must include not only structural, but also thermal and electrical considerations. Most energy storage and conversion devices are made from advanced composite materials, and they must be designed to interact and sustain their functions in multiple fields, often mechanical, electrical, electrochemical, and thermal. The functional characteristics of such materials are not only controlled by the constituent properties, but are highly dependent on the size, shape, geometry, arrangement, and interfaces between the constituent materials, the extrinsic factors controlled by processing. That is the subject of the present paper. In particular, we will focus on the design of microstructure in heterogeneous materials to manage the dielectric properties and character of such materials.