A method of preparing an antioxidant polymer includes forming or obtaining a first polymer having reactive pendant groups, where the first polymer does not include cyclic anhydride repeat units, and derivatizing the first polymer with an antioxidant. Another method of preparing an antioxidant polymer includes forming or obtaining a first polymer having reactive pendant groups and derivatizing the first polymer with an antioxidant, where the antioxidant is attached to the first polymer by an acetal, amide, amine, carbamate, carbonate, ester, ether or thioether linkage or by a carbon-carbon bond. The invention is also directed to polymers that are generally prepared by these methods, compositions that include such polymers and methods of using such polymers.