A review. This article summarizes our recent developments for H2O2- and O2-based green oxidn. reactions by polyoxometalates (POMs) and related compds. POM-based structurally controlled mol. catalysts exhibit high catalytic performance for epoxidn. and sulfoxidn. with H2O2. These mol. catalysts can be immobilized on the org.-inorg. hybrid support with covalently anchoring N-octyldihydroimidazolium cation fragments via the anion exchange. In addn., we have developed supported metal hydroxide catalysts such as Ru(OH)x/Al2O3 and Cu(OH)x/TiO2 on the basis of the information of the catalytically active sites with POMs. By using these supported metal hydroxide catalysts, novel aerobic oxidative synthesis of nitriles and amides, and efficient aerobic oxidative homocoupling of alkynes can be realized. [on SciFinder(R)]