Rifted continental margins are the product of stretching, thinning and ultimate break-up of a continental plate into smaller fragments, and the rocks lying beneath them store a record of this rifting process. Earth scientists can read this record by careful sampling and with remote geophysical techniques. These experimental studies have been complemented by theoretical analyses of continental extension and associated magmatism. Some rifted margins show evidence for extensive volcanic activity and uplift during rifting; at these margins, the record of the final stages of rifting is removed by erosion and obscured by the thick volcanic cover. Other margins were underwater throughout their formation and showed rather little volcanic activity; here the ongoing deposition of sediment provides a clearer record. During the last decade, vast areas of exhumed mantle rocks have been discovered at such margins between continental and oceanic crust. This observation conflicts with the well-established idea that the mantle melts to produce new crust when it is brought close to the Earth's surface. In contrast to the steeply dipping faults commonly seen in zones of extension within continental interiors, faults with very shallow dips play a key role in the deformation immediately preceding continental break-up. Future progress in the study of continental break-up will depend on studies of pairs of margins which were once joined and on the development of computer models which can handle rigorously the complex transition from distributed continental deformation to sea-floor spreading focused at a mid-ocean ridge.