The general isotopic anomalies in meteoritic xenon are described in detail. Where superior isotopic analyses exist, the xenon anomalies appear to be the same for all meteorites. In other cases there is fair evidence that the xenon examined is a mixture of "meteoritic" and contaminating atmospheric xenon. Two superior krypton analyses for carbonaceous chondrites show no anomalies which are significant in comparison with those for xenon. Barium from the Richardton chondrite is of normal isotopic composition. Cyclotron deuterons produce no Xe¹²⁴ in a tellurium target, although the other xenon isotopes, which are in excess in meteorites, are produced. A number of possible mechanisms for producing the general anomalies are discussed and found wanting. One of them, due to KURODA and CAMERON, calls for excess terrestrial fission xenon and for transfer of solar xenon to the atmosphere. It thus involves reasonable processes, but, as we show, requires unreasonable yields for spontaneous fission. A mechanism we propose calls for excess meteoritic fission xenon and for gross mass fractionation of terrestrial xenon. It thus produces the observed anomalies accurately, but by somewhat unlikely processes.