Continental break-up and the formation of new ocean basins is a fundamental process that shapes the surface of our planet. Continental break-up involves lithospheric extension and the generation and eruption of basalt, and so the models of basalt generation and mantle melting developed for oceanic examples are here linked to the thermal and tectonic regimes of continental melt generation. The geophysics, geochemistry, tectonics, petrology and geology of active rifting are investigated using case studies from the East African Rift and the Red Sea. Finally, the picture of continental break-up is completed with a review of the tectonic, magmatic and geodynamic processes active during the break-up of Gondwana in the Mesozoic.