Initial SE-dipping slow subduction of the Ligurian–Tethys lithosphere beneath Africa from Late Cretaceous to middle Oligocene twisting to a later faster E-dipping subduction of the subcrustal lithosphere is proposed as an efficient geodynamic mechanism to structure the arcuate Betic–Rif orogenic system. This new subduction-related geodynamic scenario is supported by a kinematic model constrained by well-dated plate reconstructions, tectonic, sedimentary and metamorphic data sets. The slow initial SE-dipping subduction of the Ligurian–Tethys realm beneath the Malaguide upper plate unit is sufficient to subduct Alpujarride and Nevado-Filabride rocks to few tens of kilometers of depth in middle Eocene times. The shift from SE- to E-dipping subduction during latest Oligocene–early Miocene was possibly caused by both the inherited geometry of the highly segmented Ligurian–Tethys domain and by the fast roll-back of the subducted lithospheric slab. The early Miocene rather synchronous multiple crustal and subcrustal processes comprising the collision along the Betic front, the exhumation of the HP/LT metamorphic complexes, the opening of the Alboran basin, its flooring by HP Alpujarride rocks and subsequent HT imprint, can be explained by the fast NW- and W-directed roll-back of the Ligurian–Tethys subcrustal lithospheric slab. The W retreat of the Ligurian–Tethys lithosphere in middle–late Miocene times could partly explain the initiation of its lateral tear and consequent subcrustal processes. From latest Miocene onward the Betic–Rif system evolved under both the northerly push of Africa resulting in tightening at crustal and subcrustal levels and by the distinct current dynamics of the steep lithospheric slab. The SW-directed scape of the Rif fold belt is one of the most striking evidences linked to the recent evolution of the squeezed Betic–Rif system between Africa and Iberia. ► Kinematic model for the Betic–Rif orogen with initial SE-dipping subduction ► Highly stretched Ligurian–Tethys lithosphere subducted beneath N-moving Africa ► Late Cretaceous to mid Oligocene slow subduction and HP metamorphic peak ► Subduction shifted to E-dipping in late Oligocene due to ocean segmentation. ► Coeval roll-back, Alboran back-arc extension and exhumation of HP rocks