High engine efficiency, comparably low pollutant emissions, and advantageous carbon dioxide emissions make lean-burn natural gas engines an attractive alternative compared to conventional diesel or gasoline engines. However, incomplete combustion in natural gas engines results in emission of small amounts of methane, which has a strong global warming potential and consequently makes an efficient exhaust gas aftertreatment system imperative. Palladium-based catalysts are considered as most effective in low temperature methane conversion, but they suffer from inhibition by the combustion product water and from poisoning by sulfur species that are typically present in the gas stream. Rational design of the catalytic converter combined with recent advances in catalyst operation and process control, particularly short rich periods for catalyst regeneration, allow optimism that these hurdles can be overcome. The availability of a durable and highly efficient exhaust gas aftertreatment system can promote the widespread use of lean-burn natural gas engines, which could be a key step towards reducing mankind’s carbon footprint.