The discovery of simple and efficient catalyst systems for the asymmetric oxofunctionalization of hydrocarbons is a challenging task of catalytic chemistry. In this paper, we give an overview of catalyst systems capable of conducting asymmetric oxygenative transformations of organic molecules and, in line with the major trend to sustainability, relying on green oxidants H₂O₂ and O₂ as the ultimate oxygen source. The full historical period of asymmetric oxidation catalysis (1970 to the present day) is covered; both transition-metal-based and organocatalytic systems are considered. The focus of this review is the catalytic properties of the existing catalyst systems, in particular stereoselectivity, activity, efficiency, and synthetic outlook. At the same time, mechanistic peculiarities of stereoselective oxygen transfer are given attention.