The present invention relates to polymer composite materials containing carbon nanotubes, particularly to those containing singled-walled nanotubes. The invention provides a polymer composite comprising one or more base polymers, one or more functionalized m-phenylenevinylene-2,5-disubstituted-p-phenylenevinylene polymers and carbon nanotubes. The invention also relates to functionalized m-phenylenevinylene-2,5-disubstituted-p-phenylenevinylene polymers, particularly to m-phenylenevinylene-2,5-disubstituted-p-phenylenevinylene polymers having side chain functionalization, and more particularly to m-phenylenevinylene-2,5-disubstituted-p-phenylenevinylene polymers having olefin side chains and alkyl epoxy side chains. The invention further relates to methods of making polymer composites comprising carbon nanotubes.