Methane monooxygenases (MMOs) mediate the facile conversion of methane into methanol in methanotrophic bacteria with high efficiency under ambient conditions. Because the selective oxidation of methane is extremely challenging, there is considerable interest in understanding how these enzymes carry out this difficult chemistry. The impetus of these efforts is to learn from the microbes to develop a biomimetic catalyst to accomplish the same chemical transformation. Here, we review the progress made over the past two to three decades toward delineating the structures and functions of the catalytic sites in two MMOs: soluble methane monooxygenase (sMMO) and particulate methane monooxygenase (pMMO). sMMO is a water-soluble three-component protein complex consisting of a hydroxylase with a nonheme diiron catalytic site; pMMO is a membrane-bound metalloenzyme with a unique tricopper cluster as the site of hydroxylation. The metal cluster in each of these MMOs harnesses O2 to functionalize the C-H bond using different chemistry. We highlight some of the common basic principles that they share. Finally, the development of functional models of the catalytic sites of MMOs is described. These efforts have culminated in the first successful biomimetic catalyst capable of efficient methane oxidation without overoxidation at room temperature.