Catalytic enantioselective oxygen transfer reactions have been a long-standing goal of synthetic chemistry. The use of molecular oxygen in these oxidations has engaged significant research efforts for decades. The present review considers the state of the art of aerobic asymmetric oxidations mediated by chiral organocatalysts and transition metal catalysts, occurring with formation of new C-O bonds, i.e. Oxygenations. The milestones and limitations of existing approaches are discussed, with focus on catalyst design and catalytic performance. The bibliography includes 41 references.