Abstract Evidence mainly from Neogene–Recent sedimentary units and penetrative structures (faults and folds) is used to constrain stress regimes in Cyprus. Following c. south-vergent folding/thrusting, a regional change to extension activated several depocentres during the Late Miocene–Early Pliocene. Fault analysis establishes that kinematic linkages existed between the four Late Miocene basins in southern and western Cyprus. During Late Pliocene(?)–Early Pleistocene time there was a switch to c. east–west left-lateral strike-slip/transpression and fault reactivation. Late Pleistocene growth folding in western coastal Cyprus is explained by reactivation of extensional faults in a left-lateral stress regime. The timing of neotectonic faulting/folding in several areas is constrained by optically stimulated luminescence dating. Existing tectonic models involving north–south collision, left-lateral strike-slip and post-collisional suture tightening are problematic in certain respects. A new model is proposed in which Late Miocene extensional basin formation relates to northward subduction coupled with rollback of the African plate. Subduction culminated in collision of the Eratosthenes Seamount, the leading edge of the African plate, with the Cyprus active margin ( c. 3 Ma). This initiated regional uplift focused on the Troodos Massif. Cyprus was by then coupled with Anatolia as it escaped westwards towards the Aegean subduction zone, giving rise to dominantly strike-slip-related structures in southern Cyprus during the Late Pliocene–Recent.