We combine observations of group and phase velocity dispersion of Rayleigh waves, of the waveform of a long-period PL phase, of Pn and Sn velocities from unreversed refraction profiles using earthquakes, and of teleseismic S-P travel time residuals to place bounds on the seismic wave velocity structure of the crust and upper mantle under Tibet. From surface wave measurements alone, the Tibetan crustal thickness can be from 55 to 85 km, with corresponding uppermost mantle shear wave velocities of about 4.4 to 4.9 km/s, respectively. The Pn and Sn velocities were determined to be 8.12¿0.06 and 4.8¿0.1 km/s, respectively, using travel time data at Lhasa from earthquakes in and on the margins of Tibet. Combining these results, the crustal thickness is most likely to be between 65-80 km with an average shear wave velocity in the upper crust less than 3.5 km/s. A synthesis of one PL waveform does not provide an additional constraint on the velocity structure but is compatible with the range of models given above. In contrast to observations obtained for eight earthquakes in the Himalaya, measurements of both teleseismic S and P wave arrival times for nine earthquakes within Tibet show unusually large intervals between P and S compared with the Jeffreys-Bullen Tables. Thus the Pn and Sn velocities apparently do not reflect high velocities in the mantle to a great depth beneath Tibet. From the dependence of the seismic velocities of olivine on pressure and temperature and from the similarity of the measured Pn and Sn velocities beneath Tibet and beneath shields and platforms, the velocities at the Moho beneath Tibet are compatible with the temperature being 250¿-300¿ higher than beneath shields and platforms, i.e., 750¿C if the temperature beneath the platforms is close to 500¿C. Such a temperature could reach or exceed the solidus of the lower crust. Simple one-dimensional heat conduction calculations suggest that the volcanic activity could be explained by the recovery of the geotherm maintained by a mantle heat flux of about 0.9 HFU at the base of the crust. If the distribution of radioactive heat production elements were not concentrated at the top of the crust, radioactive heating could also contribute significantly to the recovery of the geotherm and thus lower the required mantle heat flow. Thus the idea of a thickened crust in response to horizontal shortening is compatible both with these data and with these calculations.