GENERAL INTRODUCTIONOxidation is a fundamental technology for converting bulk chemicals into valuable materials and is also a useful tool for sophisticated functionalization of organic molecules. Thus, intensive research efforts have been devoted to the development of selective and practical oxidation methods, and a wide variety of chiral metal -based catalysts and organocatalysts have been developed for catalytic asymmetric oxidation reactions in industry and academia in the last half -century [1] . In contrast to the rapid improvement in stereoselectivity, the enhancement of atom economy [2] falls behind. While atom effi ciency (especially active oxygen content in oxygenation reactions) of stoichiometric oxidants is a factor that should be considered, most of the catalytic asymmetric oxidations still use conventional stoichiometric oxidants of low atomeffi ciency such as peracids, alkyl hydroperoxides, hypervalent iodine reagents, hypochlorite, and N -oxide compounds (Table 11.1 ). The use of such oxidants causes the formation of large amounts of undesirable waste. From the viewpoint of ecological sustainability, oxidation with a higher atom -effi cient, safe, abundant, and preferably inexpensive oxidant is favorable. Considering the requirements, molecular oxygen and hydrogen peroxide are the oxidants of choice [3] . Molecular oxygen offers a large advantage because it is abundant in air and is inexpensive. Aerobic oxidation that directly uses ambient air as an oxidant is similar to respiration in living organisms. Hydrogen peroxide is also recognized as a green oxidant. It is almost as equally atomeffi cient as molecular oxygen, and the by -product is safe and clean water. Moreover, its aqueous solution (typically 30 -35%) is inexpensive and easy to handle. Consequently, the development of catalytic asymmetric oxidations with molecular oxygen Catalytic Asymmetric Synthesis, Third Edition, Edited by Iwao Ojima