•Green catalytic oxidations of alcohols with dioxygen and hydrogen peroxide in water.•Tungsten, molybdenum and vanadium catalysts for oxidations with hydrogen peroxide.•Palladium(II) diamine complexes and supported palladium nanoparticles as catalysts.•Stable N-oxy radicals as organocatalysts for the aerobic oxidation of alcohols.•Biocatalytic aerobic oxidations mediated by laccase/TEMPO. Catalytic oxidations of alcohols, with dioxygen or hydrogen peroxide as the primary oxidant, in aqueous reaction media are reviewed. Selective alcohol oxidations with hydrogen peroxide generally involve early transition elements, mostly tungsten, molybdenum and vanadium, in high oxidation states and peroxometal complexes as the active oxidants. Aerobic oxidations, in contrast, involve oxidative dehydrogenation, usually catalyzed by late transition elements, e.g. water soluble palladium(II)-diamine complexes, or supported nanoparticles of Pd or Au as hybrid species at the interface of homogeneous and heterogeneous catalysis. Alternatively, water soluble organocatalysts, exemplified by stable N-oxy radicals such as TEMPO and derivatives thereof, in conjunction with copper catalysts, are efficient catalysts for the aerobic oxidation of alcohols. Metal-free variants of these systems, e.g. employing nitrite or nitric acid as a cocatalyst, are also effective catalysts for aerobic alcohol oxidations. Finally, enzymatic aerobic oxidations of alcohols employing oxidases as catalysts are described. In particular, the laccase/TEMPO system is receiving much attention because of possible applications in the selective oxidations of diols and carbohydrates derived from renewable resources.