The effects of terrestrial weathering on REE mobilization are evaluated for a variety of uncommon meteorites found in Antarctica and in hot deserts. The meteorites analyzed include 7 non-cumulate eucrites, 10 shergottites, 3 nakhlites, 2 lunar meteorites, 4 angrites, 10 acapulcoites, 1 winonaite, and 1 brachinite. In-situ concentration measurements of lanthanides and selected other minor and trace elements were made on individual grains by secondary ion mass spectrometry (SIMS). In Antarctic meteorites, oxidation converts Ce 3+ to Ce 4+, which is less soluble than the trivalent REE, resulting in Ce anomalies. The mineral most affected is low-Ca pyroxene. However, not all grains of a given mineral are, and distinct analyses of a single grain can even yield REE patterns with and without Ce anomalies. The effect is most pronounced for Antarctic eucrites in which Ce anomalies are observed not only in individual minerals but also in whole rock samples. Although Ce anomalies are observed in meteorites from hot deserts as well, the most characteristic signs of chemical alteration in this environment are a LREE enrichment with a typical crustal signature, as well as Sr, Ba and U contaminations. These can modify the whole rock REE patterns and disturb the isotope systematics used to date these objects. The LREE contamination is highly heterogeneous, affecting some grains and not others of a given mineral (mainly olivine and low-Ca pyroxene, the two minerals with the lowest REE concentrations). The major conduit for REE movement is through shock-induced cracks and defects, and the highest levels of contamination are found in altered material filling such veins and cracks. Meteorites that experienced low shock levels and those that are highly recrystallized are the least altered.