This chapter describes the gas barrier and dielectric properties of nanostructure polymer blends. More particularly, it relates to the incorporation of nanostructured fillers such as polyhedral oligomeric silsesquioxane (POSS) and layered silicate clays in a polymer matrix. The resulting nanostructured polymers show improved gas barrier and dielectric properties. Such properties are useful in the production of lightweight transportation bodies in the automotive industry, high-performance in the packaging industry. The dispersion of nanoparticles into a fully intercalated state is dependent on the properties of the nanoparticles and the polymer matrix. The properties of ethylene-vinyl acetate (EVA) and polyamides, nanostructured blends of EVA, nanostructured polyamide blends and POSS-blended nanostructured polymer are discussed in detail.