Selective oxidation reactions are challenging when carried out on an industrial scale. Many traditional methods are undesirable from an environmental or safety point of view. There is a need to develop sustainable catalytic approaches that use molecular oxygen as the terminal oxidant. This review will discuss the use of stable radicals (primarily nitroxyl radicals) in aerobic oxidation catalysis. We will discuss the important advances that have occurred in recent years, highlighting the catalytic performance, mechanistic insights and the expanding synthetic utility of these catalytic systems.