The present invention is directed to methods of integrating carbon nanotubes into epoxy polymer composites via chemical functionalization of carbon nanotubes, and to the carbon nanotube-epoxy polymer composites produced by such methods. Integration is enhanced through improved dispersion and/or covalent bonding with the epoxy matrix during the curing process. In general, such methods involve the attachment of chemical moieties (i.e., functional groups) to the sidewall and/or end-cap of carbon nanotubes such that the chemical moieties react with either the epoxy precursor(s) or the curing agent(s) (or both) during the curing process. Additionally, in some embodiments, these or additional chemical moieties can function to facilitate dispersion of the carbon nanotubes by decreasing the van der Waals attractive forces between the nanotubes.