Catalytic combustion of methane at 10- to 20-atm typically occurs over supported palladium oxide catalysts. Almost all investigations of methane combustion kinetics at 1-atm or higher pressures have been performed over palladium oxide, while most surface science investigations of alkane oxidation over well-defined palladium have been conducted with oxygen chemisorbed over metallic palladium. At low pressure alkane oxidation rates are characterized as "very fast" while some authors state that metallic Pd is "inactive" for methane oxidation. The thermodynamics and kinetics of light alkane combustion over metallic palladium will be reviewed in this paper. A few specific rate measurements above the transition temperature under industrially relevant pressures (~875°C) are characterized by very high apparent activation energies with rates typically factors or two or more lower rates at the transition than rates over the oxide. The few published specific rate measurements at or above 1-atm pressure are consistent with a vacancy/ensemble description of methane combustion over metallic palladium. High concentrations of vacancies in monolayers of chemisorbed oxygen can lead to very high rates in both high pressure/high temperature and low pressure/low pressure regimes. The contractictory description of relative methane combusiton rates is explained by the absence of vacancies in the chemisorbed layer at high pressures and low temperatures. Coarsening of metallic palladium under high temeprature combustion conditions will also be reviewed including the relevance of small Pd particle migration and the classic vapor transport (Ostwalt ripening) process as first described many years ago by Wagner et. al.