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.