Unusual scattering effects from tiny spherical particles may be obtained when concentric shells are designed by pairing together "complementary" double-negative, single-negative, and/or standard double-positive materials. By embedding these highly polarizable scatterers in a host medium one can achieve a bulk medium with interesting effective parameters. Some physical insights and justifications for the anomalous polarizability of these concentric spherical nanoparticles and the effective parameters of the bulk composite medium are discussed.