Rifted margins mark a transition from continents to oceans and contain in their architecture a record of their rift history. Recent investigations of rift architecture have suggested that multiphase deformation of the crust and mantle lithosphere leads to the formation of distinct margin domains. The processes that control transitions between these domains, however, are not fully understood. Here we use high-resolution numerical simulations to show how structural inheritance and variations in extension velocity control the architecture of rifted margins and their temporal evolution. Distinct domains form as extension velocities increase over time and deformation focuses along lithosphere-scale detachment faults, which migrate oceanwards through re-activation and complex linkages of prior fault networks. Our models demonstrate, in unprecedented detail, how faults formed in the earliest phases of continental extension control the subsequent structural evolution and complex architecture of rifted margins through fault interaction processes, hereby creating the widely observed distinct margin domains.