The extension of the lithosphere, controlling the development of rifted basins, is driven by a combination of plate-boundary forces, frictional forces exerted on the base of the lithosphere by the convecting asthenosphere and deviatoric tensional stresses developing over upwelling branches of the asthenospheric convection system. Although mantle plumes are not a primary driving force of rifting, they play an important secondary role by weakening the lithosphere and by controlling the level of rift-related volcanic activity. A distinction between "active" and "passive" rifting is only conditionally justified.The extension of the lithosphere, depending on its rate and magnitude, and the potential temperature of the asthenosphere, can cause by adiabatic decompression partial melting of the lower lithosphere and upper asthenosphere. In rift systems, the level and timing of volcanic activity is highly variable. The lack of volcanic activity implies "passive" rifting. An initial "passive" rifting stage can be followed by a more "active" one during which magmatism plays an increasingly important role. Magmatic destabilization of the Moho may account for the frequently observed discrepancy between upper and lower crustal extension factors. Combined with evidence for thermal thinning of the mantle-lithosphere, this suggest that the volume of the lithosphere is not necessarily preserved during rifting as advocated by conventional stretching models.The structural style of rifts is controlled by the rheological structure of the lithosphere, the availability of crustal discontinuities that can be tensionally reactivated, the mode (orthogonal or oblique) and amount of extension, and the lithological composition of pre- and syn-rift sediments. Simple-shear extension prevails in rifts that subparallel the structural grain of the basement. Pure-shear extension is typical for rifts cross-cutting the basement grain. Pre-existing crustal and mantle-lithospheric discontinuities contribute to the localization of rift systems.The duration of the rifting stage of extensional basins is highly variable. Stress field changes can cause abrupt termination of rifting. In major rift systems, progressive strain concentration on the zone of future crustal separation entails abandonment of lateral rifts. Depending on constraints on lateral block movements, crustal separation can be achieved after as little as 9 My and as much as 280 My of rifting activity.Syn-rift basin subsidence is controlled by isostatic adjustment of the crust to mechanical stretching of the lithosphere, its magmatic inflation and thermal attenuation of the mantle-lithosphere.Post-rift basin subsidence is governed by thermal reequilibration of the lithosphere-asthenosphere system. Deep-seated thermal anomalies related to syn-rift pull-up of the asthenosphere-lithosphere boundary have decayed after 60 My by about 65% and after 180 My by about 95%. The magnitude of post-rift subsidence is a function of the rift-induced thermal anomaly and crustal density changes, the potential temperature of the asthenosphere and initial water depths. Intraplate stresses can have an overprinting effect on post-rift subsidence. Stretching factors derived from post-rift subsidence analyses must be corrected for such effects. © 2003 Elsevier B.V. All rights reserved.