A large fraction of surface extension on Mars occurred at segmented grabens having width/length ratios akin to oceanic rifts on Earth. Association with volcanic landforms such as pit craters clearly suggests interconnection between tectonic and magmatic processes. A Martian rift evolution model is proposed on the basis of new geomorphological and structural interpretations of imagery, high-resolution digital elevation models (DEMs), scaled experimental modeling and three-dimensional boundary element modeling of magmatic and tectonic processes, and a comparison with terrestrial rifts. The DEMs were obtained from Mars Observer Laser Altimeter, Viking Orbiter stereo images, or a combination of both. Comparison of terrestrial rifts included Afar, Iceland, and the East Pacific Rise. The ambient extensional stress field induced by regional body forces is combined at depth with decompression melting and mantle plume thermal anomaly, resulting in emplacement of elongated magma reservoirs along the grabens. Injection of dikes above the reservoirs and flood basalt eruption result in a reservoir underpressurization of up to hundreds of MPa and induces surface collapse. Each collapse event is associated with an eruption of volcanic volumes akin to those of individual flow eruptions in large terrestrial igneous provinces. The geometry and mechanisms of graben formation and surface collapse are described and used to infer reservoir depth and width. We conclude from this study that giant dike swarms akin to typical giant terrestrial dike swarms are unlikely to underlie the volcanic Martian grabens on the basis one graben-one dike. Rather, every volcanic graben segment appears to own a local dike swarm perhaps analogous to the dike swarms in the Icelandic fissure zones.