The present invention is directed to methods of purifying carbon nanotubes (CNTs). In general, such methods comprise the following steps: (a) preparing an aqueous slurry of impure CNT material; (b) establishing a source of Fe.sup.2+ ions in the slurry to provide a catalytic slurry; (c) adding hydrogen peroxide to the catalytic slurry to provide an oxidative slurry, wherein the Fe.sup.2+ ions catalyze the production of hydroxyl radicals; and (d) utilizing the hydroxyl radicals in the oxidative slurry to purify the CNT material and provide purified CNTs.