Using receiver-functions and surface-wave dispersion curves, we study the crustal and upper-mantle structure of Saudi Arabia. Our results reveal first-order differences in crustal thickness between the Arabian Shield in the west and the Arabian Platform in the east. Moho depths generally increase eastward, while crustal thickness varies strongly in the west over the volcanic regions and near the Red Sea. Localized zones of increased P-wave speed in the west may indicate solidified magmatic intrusions within the area of recent volcanism. Our receiver-function analysis for deep converted phases reveals that the transition zone thickness between the 410 km and the 660 km discontinuities is not anomalously thinned, refuting the hypothesis of a small localized mantle plume as the origin for the volcanic activity in western Saudi Arabia. Our results suggest that the volcanism in western Arabia may be due to the lithospheric mantle being heated from below by lateral flow from the Afar and (possibly) Jordan plumes. This triggers localized melts that ascend adiabatically through the lithosphere as magma diapirs. Recent xenolith measurements that provide information on temperatures and depths of melting are overall consistent with this hypothesis. However, further dedicated localized tomographic studies are needed to decipher the details of the origin of the volcanism and its relation to the overall geodynamics of the region.