Most advances and commercial successes of polymer/inorganic nanocomposites rely only on the dispersion of nanoparticles in a polymer matrix. Such approaches leave untapped opportunities where performance can be improved by controlling the larger length-scale structures. Here, we review selected examples where the hierarchical structure (from millimeter to nanometer) is tailored to control the transport properties of the materials, giving rise to marked property enhancements, relevant to dielectric materials for power capacitors. These examples address composite structures that are self-assembled, both at the nm and the micron scales, and, thus, can be produced using standard industrial practices. Specifically, polyethylene (PE) blends or poly(vinylidene fluoride) (PVDF) copolymers are reinforced with nanofillers; these composites are designed with high filler orientation, which yielded marked improvements in electric-field breakdown strength and, consequently, large improvements in their recoverable energy densities.