Palladium-based catalysts are widely applied in exhaust catalytic converter and catalytic combustion systems. The mechanism for methane oxidation on a Pd-based catalyst is complex. Catalyst activity is influenced by variations in the process pressure and temperature, by the gas mixture composition, by the type of support and various additives, and by pretreatment under reducing or oxidizing atmospheres. In this paper, we review the literature on supported Pd catalysts for combustion of methane. The mechanisms involved are discussed taking into consideration the oxidation/reduction mechanisms for supported palladium, poisoning, restructuring, the form of oxygen on the surface, methane activation over Pd and PdO phases, and transient behavior. Our review helps explain the array of experimental results reported in the literature.