Oxidative transformations are of paramount importance in nature and in synthetic laboratories in both academia and industry. With the aid of catalysis, bio-inspired aerobic oxidation has become a sustainable and economical alternative to the well-established stoichiometric processes. In this chapter we present an introductory discussion on the development of catalysis, the history and chemistry of oxygen, the importance of aerobic oxidation reactions, its many application areas and the challenges associated with their chemistry, all within the premises of sustainability and green chemistry.