Abstract The Paleozoic Variscan orogen in Europe has a markedly circuitous trace for which several different origins have been postulated, including deformation around promontories on the colliding continental margins, extrusion within the collision zone, folding of a ribbon continent and collision with a substantial dextral component. Adopting the latter assumption, unfolding of the large, steeply plunging folds (‘oroclines’) of Iberia and the Moroccan Meseta requires more than 4000 km of dextral lateral translation of Laurussia with respect to Gondwana. Constraints on the age of the folding require that this lateral translation occurred in mid-late Carboniferous time. Significant dextral translation of Laurussia with respect to Gondwana late in the Variscan collision is supported by palaeomagnetic data for the two supercontinents, although the exact timing of this relative motion is not well constrained due to large uncertainties in the palaeomagnetic pole positions. Our palinspastic reconstruction of the major Variscan folds of Iberia places the rocks of the South Portuguese Zone of western Iberia adjacent to the Rhenish Massif; for instance, as part of Avalonia. By the same token, the Sehoul Block in the Moroccan Meseta probably originated at the western end of Cadomia, although nothing in our analysis precludes it also being derived from Avalonia.