During and mainly after the Tertiary continental collisions, regions of extension and subsidence developed within the Alpine-Mediterranean orogenic belt in the rear part of the contemporaneously active arcs. Mediterranean back-arc basins are characterized by a hot upper mantle, overlain by crust transitional from continental to oceanic, which reflects their different stages of maturation. The four basins considered here are, in order of increasing maturity, the Pannonian Basin, the Aegean Basin, the Alboransouth Balearic Basin and the Tyrrhenian Basin. Back-arc extension is not a rigid plate opening but rather an areal expansion associated with progressive bending of the arc. The most successful models suggested for the evolution of Mediterranean back-arc basins imply updoming of the asthenosphere accompanied by lithospheric attenuation, stretching and dyke intrusion. The force behind asthenospheric updoming is under debate; active and passive mechanisms have been suggested. It seems, however, certain that gravity plays an important role in initiating and maintaining back-arc extension. Basin subsidence is an isostatic response to structural changes of the lithosphere and to conductive decay of the associated heat anomaly. A quantitative model for basin formation can be obtained only if the subsidence history is well documented.