A long-standing challenge in tectonics is to evaluate the role of inheritance and define the initial conditions of a geodynamic system, which are prerequisites to understand and model its evolution with some accuracy. Here we revisit the concept of “inheritance” by distinguishing “interface shape inheritance”, which includes the transient thermal state and gravitational potential energy, and “persisting inheritance”, which encompasses long-lasting structural and compositional inheritance. This new approach allows us to investigate, at each stage of a Wilson Cycle, the interplay between inheritance (innate/“genetic code”) and the physical processes at play (extension/compression, magmatism etc.). 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 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 mature rifted margins in the west to an immature and segmented hyperextended rift in the east. However, different models have been proposed to explain the preceding rifting and its influence on the subsequent reactivation. Results from the OROGEN project highlight the sequential reactivation of rift-inherited decoupling horizons and identify the specific role of exhumed mantle, hyperextended and necking domains during compressional reactivation. They also highlight the contrasting fate of rift segment centresversussegment 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 collision, which may explain the higher complexity of internal parts of orogenic systems with respect to their external parts. In contrast, when the system involved in the orogeny is more mature, the orogenic evolution is 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 and may also explain why most numerical models can reproduce mature orogenic architectures with a better accuracy compared to those of initial collisional stages. 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.