Selective oxidation reactions have extraordinary value in organic chemistry, ranging from the conversion of petrochemical feedstocks into industrial chemicals and polymer precursors to the introduction of heteroatom functional groups into pharmaceutical and agrochemical intermediates. Molecular oxygen (O2) would be the ideal oxidant for these transformations. Whereas many commodity-scale oxidations of simple hydrocarbon feedstocks employ O2 as an oxidant, methods for selective oxidation of more complex molecules bearing diverse functional groups are often incompatible with existing aerobic oxidation methods. The latter limitation provides the basis for our interest in the development of new catalytic transformations and the elucidation of mechanistic principles that underlie selective aerobic oxidation reactions. One challenge inherent in such methods is the incommensurate redox stoichiometry associated with the use of O2, a four-electron oxidant, in reactions that achieve two-electron oxidation of organic molecules. This issue is further complicated by the use of first-row transition-metal catalysts, which tend to undergo facile one-electron redox steps. In recent years, we have been investigating Cu-catalyzed aerobic oxidation reactions wherein the complexities just noted are clearly evident. This Account surveys our work in this area, which has emphasized three general classes of reactions: (1) single-electron-transfer reactions for oxidative functionalization of electron-rich substrates, such as arenes and heterocycles; (2) oxidative carbon-heteroatom bond-forming reactions, including C-H oxidations, that proceed via organocopper(III) intermediates; and (3) methods for aerobic oxidation of alcohols and amines that use Cu(II) in combination with an organic redox-active cocatalyst to dehydrogenate the carbon-heteroatom bond. These reaction classes demonstrate three different pathways to achieve two-electron oxidation of organic molecules via the cooperative involvement of two one-electron oxidants, either two Cu(II) species or Cu(II) and a nitroxyl cocatalyst. They show the ability of Cu to participate in traditional organometallic steps commonly associated with precious-metal catalysts, such as C-H activation and reductive elimination, but also demonstrate the accessibility of reaction steps not typically associated with precious-metal catalysts, such as single-electron transfer. Many of the Cu-catalyzed reactions offer advantages over analogous two-electron oxidation reactions mediated by palladium or other noble metals. For example, carbon-heteroatom oxidative coupling reactions in the first two reaction classes noted above are capable of using O2 as the terminal oxidant, while analogous reactions with Pd commonly require less desirable oxidants, such as hypervalent iodine or electrophilic halogen sources. In addition, the alcohol and amine oxidations in the third reaction class are significantly more efficient and show much broader scope and functional group tolerance than related Pd-catalyzed reactions. Th...