This review summarizes the current state of polymer composites used as dielectric materials for energy storage. The particular focus is on materials: polymers serving as the matrix, inorganic fillers used to increase the effective dielectric constant, and various recent investigations of functionalization of metal oxide fillers to improve compatibility with polymers. We review the recent literature focused on the dielectric characterization of composites, specifically the measurement of dielectric permittivity and breakdown field strength. Special attention is given to the analysis of the energy density of polymer composite materials and how the functionalization of the inorganic filler affects the energy density of polymer composite dielectric materials.