Continental rifting is a geodynamic process that involves the breakup of the crust and may eventually evolve to seafloor spreading. Although it is often assumed to be a product of orthogonal divergence, continental rifting may result from oblique extension, and in several cases, it is related to the rotation of plates or crustal blocks about a vertical axis. This implies the occurrence of rifts with straight but not parallel margins and rift axis-parallel gradients in extension velocity and amount of strain. The effects of rift propagation through the continental crust has only recently started to be addressed, and even less investigated is the interaction between rift propagation and inherited crustal fabrics. We have studied this issue by carrying out a series of analog laboratory experiments. Modeling results suggest that inherited linear discontinuities in the model brittle upper crust that are oriented above a threshold angle (≥45°) from the orthogonal to the rift axis have the ability to interact with rift-related structures. Depending on their orientation, such inherited discontinuities are reactivated as either transfer zones or rift-bounding faults. We compare our models with four natural prototypes in which rift propagation is likely to have occurred (the Trans Mexican Volcanic belt, the Gofa Province, the Gulf of Suez, and the Kenya Rift). For each case study, we show how the kinematics of propagating rifts is comparable to our model results, and we provide insights into how rift-related deformation may interact with inherited crustal fabrics. Plain Language Summary When the continental Earth's crust breaks due to tensional tectonic forces, deep depressions called continental rifts form. Over geological time, these features may ultimately evolve to oceans. This process is often assumed to occur symmetrically, but it has been shown that this is rarely the case. Indeed, continental rifting is often generated by the rotation of tectonic plates, which induces changes in the extension velocity along the length of the rift. In order to understand the evolution of many natural rifts, it is also important to determine how rifting interacts with existing discontinuities in the crust (e.g., faults). This issue has only been recently addressed by laboratory experimental models, in which natural processes are simulated at reduced time and length scales, using appropriate analog materials to replicate the physical properties of natural rocks. We have performed a series of experiments that test this interaction, discovering that preexisting faults can have a strong influence on the formation and evolution of continental rifts. To verify this correlation, we have compared our models with four (Mexico, Ethiopia, Egypt, and Kenya) natural cases, finding that older faults have often influenced the rifting process and the resulting structure.