Seismic anisotropy provides evidence for the physical state and tectonic evolution of the lithosphere. We discuss the origin of anisotropy at various depths, and relate it to tectonic stress, geotherms and rheology. The anisotropy of the uppermost mantle is controlled by the orthorhombic mineral olivine, and may result from ductile deformation, dynamic recrystallization or annealing. Anisotropy beneath young orogens has been measured for the seismic phase Pn that propagates in the uppermost mantle. This anisotropy is interpreted as being caused by deformation during the most recent thermotectonic event, and thus provides information on the process of mountain building. Whereas tectonic stress and many structural features in the upper crust are usually orientated perpendicular to the structural axis of mountain belts, Pn anisotropy is aligned parallel to the structural axis. We interpret this to indicate mountain-parallel ductile (i.e. creeping) deformation in the uppermost mantle that is a consequence of mountain-perpendicular compressive stresses. The preferred orientation of the fast axes of some anisotropic minerals, such as olivine, is known to be in the creep direction, a consequence of the anisotropy of strength and viscosity of orientated minerals. In order to explain the anisotropy of the mantle beneath young orogens we extend the concept of crustal 'escape' (or 'extrusion') tectonics to the uppermost mantle. We present rheological model calculations to support this hypothesis. Mountain-perpendicular horizontal stress (determined in the upper crust) and mountain-parallel seismic anisotropy (in the uppermost mantle) require a zone of ductile decoupling in the middle or lower crust of young mountain belts. Examples for stress and mountain-parallel Pn anisotropy are given for Tibet, the Alpine chains, and young mountain ranges in the Americas. Finally, we suggest a simple model for initiating mountain parallel creep.