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The Rio do Peixe Basin is part of a series of aborted Cretaceous rifts formed within the Proterozoic Borborema Province, onshore NE Brazil in response to rifting between Africa and South America. The basin is remarkably well‐imaged and comprises fault‐bounded depocentres, the main ones being the NE‐oriented Brejo das Freiras and the E–W‐oriented Sousa half‐grabens. These grabens and their bounding faults are influenced by Neoproterozoic basement shear zones and present a complex framework of secondary normal faults and folds. Recent workers also interpret large reverse faults and regional post‐rift shortening driven by far‐field stresses from the Andes. For those reasons, the basin represents an ideal setting to investigate the multiphase history of rift basins. We thus combine borehole‐calibrated 2D and 3D seismic and magnetic data with section restoration and numerical modelling to investigate the architecture and evolution of this basin. We aim to understand: (i) the controls of the basement fabric in 3D fault architecture and kinematics and (ii) how syn‐rift faults controlled the geometry and development of fault‐related folds. By doing this, we also investigate the timing, kinematics, and magnitude of inversion in the basin to explore its multiphase history. We demonstrate that (i) the basement fabric controlled not only the strike of faults but also their geometry and polarity at depth, (ii) folds in the syn‐rift sequence are attributed simply to syn‐rift extension along stepped and/or curved faults, and (iii) inverted and/or reverse faults occur within the basin, but these are minor and appear to have formed during rifting. We explain this minor inversion by a change in plate kinematics related to the onset of the nearby transform margin to the north. These results have implications for understanding the 3D evolution of oblique grabens, the role of structural inheritance, and the recognition of inversion‐ versus extension‐related folds in rift basins worldwide. [ABSTRACT FROM AUTHOR]