Continental rifting is a major plate tectonic process in which the lithosphere stretches and thins, eventually causing continents to break apart by creating two conjugate rifted margins. Continental rifts often emerge in places that have been shaped by prior orogeny. The correlation between ancient orogenic belts and young rift systems highlights the importance of orogenic inheritance in shaping the complexities of rift and rifted margins alike. However, there is limited geological data from offshore domains of rifted margins, which challenges the understanding of the role of inherited orogenic structures. In addition, the issue is further complicated by the diverse nature of orogenic inheritance, characterized by variations in thermal state, compositional properties, and structural complexity across multiple scales, along with the superimposed phenomenon of subsequent extensional processes that reactivate inherited structures. This raises the critical question of how orogenic inheritance influences the evolution of rifts and the final architecture of rifted margins. In this thesis, a geodynamic numerical modelling approach is employed, integrating the thermomechanical modelling software ASPECT and the landscape evolution code FastScape to simulate the formation of orogens and rifts within the context of the Wilson Cycle. To this aim, I conduct so-called "accordion models" that involve a first phase of shortening that is followed by a phase of extension. In contrast to geological interpretation, this numerical modelling offers the advantage of generating orogenic inheritance in a self-consistent way that allows to directly quantify geological processes. Furthermore, because this coupled numerical model incorporates erosion and sedimentation, it allows for the exploration of feedback mechanisms between tectonic and surface processes. Finally, all involved parameters can be controlled, enabling detailed analysis of specific types of inheritance over the entire evolution of plate convergence and divergence. I demonstrate the applicability of these numerical models by comparing results to selected natural rifted margins worldwide. The first chapter of this thesis provides a short introduction to the research topic. I summarize main results of previous work and isolate remaining knowledge gaps. In addition, this chapter introduces the numerical modelling software used in this thesis. In the second chapter, I present two-dimensional numerical modelling where I systematically alter the velocity boundary conditions across temporal stages. Hence the model simulates successive phases of continental collision, post-orogenic collapse, continental rifting, and ultimately continental breakup, as observed in the South China Sea (SCS), a marginal basin in South East Asia. I successfully generate rifted margin architectures that align with geophysical observations in the SCS. To explore the role of orogenic inherited structures more broadly, I present alternative model scenarios incorporating variations in shortening velocities, surface erosion efficiency, and lithosphere strength. I analyze these scenarios and find that orogenic inheritance governs the reactivation of thrust faults, with continental breakup consistently occurring in regions formerly characterized by a thick crustal root. Third, I investigate the combined impact of orogenic inheritance and surface processes on the exhumation of lower crust at rifted margins, an enigmatic finding at many rifted margins. I simulate an initial phase of orogeny followed by continental breakup and vary the syn-orogenic erosion efficiencies to understand their influence on rifted margin architecture. These models clearly show that the erosion of mountain belts thins the upper crust, reducing the upper-to-lower crustal ratio prior to rifting. This process facilitates the exhumation of lower crustal material during extension, exposing it at the Earth’s surface along the footwall of normal faults. This finding leads me to propose a new conceptual model to explain lower crustal exhumation observed at rifted margins worldwide, including the northern margin of the South China Sea, the Gulf of Lion, the Aegean Sea, and the Norwegian margin. The fourth thesis chapter, focusses on the comparison of rift evolution in both simple homogeneous lithosphere and accordion models incorporating orogenic inheritance. By varying the rheological properties and surface erosional efficiency, I reproduce a variety of rifted margin architectures. Through quantitative analysis of the model results, I find that models with pre-rift orogenic inheritance reduce the far-field forces required for rift initiation, delay continental breakup, and result in wider rifted margins compared to homogeneous lithosphere models. Additionally, the application of a healing process to eliminate structural inheritance and the incorporation of a phase of tectonic quiescence to remove transient thermal inheritance allows investigation of the relative roles of different types of inheritance: structural inheritance predominantly controls rift initiation forces, margin width, and breakup location, while thermal inheritance governs crust-mantle interactions, significantly influencing rift migration, breakup timing, and margin symmetry. I also find that compositional inheritance, defined by rheological interfaces, consistently dominates, producing asymmetric rifted margins. These findings, validated through comparisons with natural examples, provide new insights into the broader implications of different orogenic inheritance types for rift system evolution. Finally, in Chapter 5, I provide concluding remarks and an outlook for potential future work where I develop 3D modelling approaches. By including a periodic boundary, I could explore rifted margin architectures simultaneously impacted by oblique extension and orogenic inheritance. (See Chapter 5.2). With these findings, I hope to improve our understanding of orogenic inheritance on rifted margin formation. Further development of geodynamic software accounting for even more realistic process in conjunction with detailed comparison with observational data may help to explore the dynamic process interaction that shape rifts and rifted margins.