The study of the deep structure and evolution of passive continental margins is important for the understanding of rifting processes and the formation of associated sedimentary basins. Since the classical models of McKenzie (1978) and Wernicke (1985), understanding how passive continental margins form, that is to say mainly the way that continental lithosphere is thinned leading to subsidence, remains one of the main challenges in the Earth sciences. Many recent observations and discoveries have modified our basic views of margin formation. The conservational models paradigm (i.e., simple shear, pure shear, or polyphase models), which exclude exchanges between lower continental crust and upper mantle and which are usually proposed to explain lithospheric stretching and consequent crustal thinning of passive continental margins, fail to completely explain all these observations. Furthermore, these models imply a large amount of horizontal movement, movements not observed in the field. In consequence, new concepts need to be built and tested.