A functionalized carbon fiber having covalently bound on its surface a partially cured epoxy or amine-containing sizing agent, wherein at least a portion of epoxide or amine groups in the sizing agent are available as uncrosslinked epoxide or amine groups, which corresponds to a curing degree of epoxide or amine groups of no more than about 0.6. Composites comprised of these functionalized carbon fibers embedded in a polymeric matrix are also described. Methods for producing the functionalized carbon fibers and composites thereof are also described.