On Mars, Xe isotopes in the present atmosphere are mass fractionated relative to their primordial composition from in situ measurement of the Curiosity Rover at Gale Crater, Mars. Paleo-atmospheric Xe trapped in the Martian regolith breccia NWA 11220 is mass-dependently fractionated relative to solar Xe by ~16.2‰. The extent of fractionation is comparable for Mars and Earth, which may be compelling evidence that hydrodynamic escape also occurred in the Mars history. The regolith breccia NWA7084 and the >4 Ga orthopyroxene ALH84001 Martian meteorites trap ancient Martian atmospheric gases with little if any Xe isotopic fractionation relative to modern Martian atmospheric Xe. Alternative models for Mars consider that the isotopic fractionation and escape of Mars atmospheric Xe occurred very early in the planet's history and ceased around a few hundred million years after planetary formation rather than continuing during its evolutionary history