Aromatic and aliphatic sulfides are oxidized to sulfoxides or sulfones in high yield with 30% hydrogen peroxide under organic solvent- and halogen-free conditions. Dialkyl and alkyl aryl sulfides are cleanly oxidized to sulfoxides using aqueous hydrogen peroxide without catalysts. The best catalyst for the sulfone synthesis consists of sodium tungstate, phenylphosphonic acid, and methyltrioctylammonium hydrogensulfate. Co-existing primary or secondary alcohol or olefinic moieties are unaffected under such conditions.