Selective aerobic oxidation of organic molecules is a fundamental and practical challenge in modern chemistry. Effective solutions to this problem must overcome the intrinsic reactivity and selectivity challenges posed by the chemistry of molecular oxygen, and they must find application in diverse classes of oxidation reactions. Palladium oxidase catalysis combines the versatility of Pd(II)-mediated oxidation of organic substrates with dioxygen-coupled oxidation of the reduced palladium catalyst to enable a broad range of selective aerobic oxidation reactions. Recent developments revealed that cocatalysts (e.g. Cu(II), polyoxometalates, and benzoquinone) are not essential for efficient oxidation of Pd(0) by molecular oxygen. Oxidatively stable ligands play an important role in these reactions by minimizing catalyst decomposition, promoting the direct reaction between palladium and dioxygen, modulating organic substrate reactivity and permitting asymmetric catalysis.