The aim of this paper is to provide a conceptual framework that integrates the role of inheritance in the study of rifts, rifted margins and collisional orogens based on the work done in the OROGEN project, which focuses on the Biscay-Pyrenean system. The Biscay-Pyrenean rift system resulted from a complex multistage rift evolution that developed over a complex lithosphere pre-structured by the Variscan orogenic cycle. There is a general agreement that the Pyrenean-Cantabrian orogen resulted from the reactivation of an increasingly mature rift system along-strike, ranging from a mature rifted margin in the west to an immature and segmented hyperextended rift in the east. However, different models have been proposed to explain the preceding syn-rift evolution and its influence on the subsequent reactivation. Results from the OROGEN project show a sequential reactivation of rift inherited decoupling horizons and identify the specific role of exhumed mantle, hyperextended and necking domains during reactivation. They also highlight the contrasting fate of segment centres vs. segment boundaries during convergence, explaining the non-cylindricity of internal parts of collisional orogens. Results from the OROGEN project also suggest that the role of inheritance is more important during the initial stages of subduction and collision, which may explain the complexity of internal parts of orogenic systems. In contrast, once tectonic systems get more mature, orogenic evolution becomes mostly controlled by first-order physical processes as described in the Coulomb Wedge theory for instance. This may account for the simpler and more continuous architecture of external parts of collisional orogens. It may also explain why most numerical models can reproduce mature orogenic and rift architectures with better accuracy compared to the initial stages of such systems. Thus, while inheritance may not explain steady-state processes, it is a prerequisite for comprehending the initial stages of tectonic systems. The new concepts developed from the OROGEN research are now ready to be tested at other orogenic systems that result from the reactivation of rifted margins, such as the Alps, the Colombian cordilleras and the Caribbean, Taiwan, Oman, Zagros or Timor.