The subject invention provides synthetic compounds, and compound complexes having catalytic activities towards oxidation or oxygenation, and/or dehydrogenation of various substrates comprising C−H bonds. The catalysts of the subject invention comprise a dinuclear Cu(I)/Cu(II) center that can convert between a resting state and a reactive species. The subject invention also provides methods of using such catalysts for the oxidation of substrates comprising C−H bonds, e.g., hydrocarbons, to synthesize chemicals for use as pharmaceuticals and industrial feedstock.