Potassic volcanism has been widespread and semi-continuous on the Tibetan plateau since ∼13 Ma, post-dating the erogenic thickening of the India-Asia collision. Volcanism may have commenced slightly earlier (∼16-20 Ma) in the southern portion of the plateau and then ceased around 10 Ma. The dominant lavas are pyroxene- and plagioclase-phyric shoshonites with subordinate occurrences of dacites and rhyolites. Their mineralogy reflects crystallization from high-temperature (≤1100°C) magmas which had elevated oxygen and water fugacities. Geochemically, they are characterized by relatively low TiO2, Al2O3 and Fe2O3, and high Na2O, coupled with variable abundances of compatible trace elements and very high contents of incompatible trace elements. Normalized incompatible element patterns have marked negative Nb, Ta and Ti anomalies whereas K2O appears to be buffered at ∼4% over a wide range of SiO2. Isotope data show a relatively broad and enriched range of 87Sr/86Sr (0·7076-0·7106) at more restricted εNd (-5·2 to -8·1). Pb isotopes are characterized by a range of 207Pb/204Pb (15·51-15·72) and 208Pb/204Pb (38·67-39·30) at very uniform 206Pb/204Pb (18·39-18·83), leading to vertical arrays. Volcanics from the southern parts of the plateau have more primitive isotopic compositions: 87Sr/86Sr 0·7048-0·7080, εNd 1·4 to -3·3, 206Pb/204Pb 18·48-18·67, 207Pb/204Pb 15·59-15·68 and 208Pb/204Pb 38·73-38·98. In general, the geochemical and isotopic data most closely approximate partial melting arrays, although fractionation processes have clearly operated. The isotopic ratios and the enrichment of incompatible elements and LREE/HREE cannot be derived from a depleted mantle source via a single-stage melting process. Instead, a metasomatized, garnet peridotite source containing ∼6% phlogopite is required and this is inferred to lie within the lithospheric mantle. The enrichment in incompatible elements in this source must have been sufficiently ancient to generate the observed isotopic ratios, and Nd depleted mantle model ages suggest this was Proterozoic in age (∼1·2 Ga), whereas Pb model ages record an Archaean event, suggesting the source had a multi-stage enrichment history. The negative Ta, Nb and Ti anomalies and low Rb/Ba suggest that metasomatism may have occurred during an ancient subduction episode. The high 208Pb/204Pb, 207Pb/204Pb and low Nb/U, Ce/Pb of the Tibetan shoshonites are distinct from ocean island basalts. Thus, if convectively removed lithospheric mantle provides a source for ocean island basalts, it must differ significantly from the source of the Tibetan shoshonites. A lithospheric mantle source for the volcanism places important constraints on geodynamic models for the evolution of the Tibetan plateau and the India-Asia collision. For likely thermal structures beneath the plateau, the temperatures required to trigger melting within the lithospheric mantle can only be plausibly obtained if the lower parts of the lithospheric mantle were removed by convective thinning. This is consistent with recent models which invoke the same process to explain the current elevation and extensional deformation of the plateau. The age data suggest this occurred at ∼13 Ma and the duration of volcanism may be explained by continued conductive heating since that time. Poorly sampled but slightly older volcanics from the southern portions of the plateau may indicate that convective thinning began in the south and migrated northwards. Rapid uplift of the plateau may have resulted in increased rates of chemical weathering, which led to global cooling, as indicated by oxygen isotope data from Atlantic sediments.