Oxidation of different groups of organic compounds, with hydroperoxides catalyzed by non-heavy metal containing low-molecular-weight compounds and enzymes is reviewed. This article is concentrated mainly on the hydrogen peroxide and tert-butyl hydroperoxide, however other less common hydroperoxides are also mentioned. Since hydroperoxides themselves are inactive toward most of the organic substrates, in situ activation of the oxidant is necessary. For this purpose various activators have been applied in stoichiometric or catalytic amounts. The carboxylic acids, nitriles, amides and urea are representative for the first category. The organocatalysts such as-halo carbonyl compounds, ketones, imines, iminium salts, nitroxyl radicals and polyaminoacids, selenium compounds and enzymes are presented. They are involved in oxygen, and electron transfer processes whose mechanisms are briefly discussed, and their applications in laboratory and industrial synthesis are indicated.