Abstract We present the results of three-dimensional numerical experiments designed to study the response of a layer of crustal material subjected to convergence through an imposed basal velocity discontinuity and to surface processes (erosion/sedimentation). We focus on the three-dimensional response of the system arising from the finite width of the imposed velocity discontinuity. In particular, we describe the complex structures that develop around the wedge and their interactions with the loading/unloading produced by the surface processes. We show that the pro- and retro-shear zones that develop in a doubly-vergent two-dimensional wedge curve around the end of the velocity line-discontinuity to merge into the strike-slip structure that naturally develop, i.e. as a consequence of the imposed boundary conditions, along the edge of the wedge. Along the retro-shear zone the stress orientation rotates along a vertical axis, which implies that the retro-shear zone is a pure thrust along all of its curved length, whereas, along the pro-shear zone stresses rotate along a horizontal axis, which, in turn, implies that the pro-shear zone progressively evolves towards an oblique thrust in its curved section. Furthermore, the outward motion (i.e. perpendicular to the direction of imposed shortening) along the curved section of the retro-shear zone is accommodated by oblique extension along a secondary, kinked structure antithetic to the retro-shear zone. We also show the complex evolution of the wedge when ductile flow and ductile strain softening is activated by increasing the imposed basal temperature. In this situation, the wedge is broader as structures develop at finite distances on either side of the line-discontinuity and its dynamics resembles more that of a ‘vise-like’ orogen. At the surface, a flat plateau forms that accumulates sediment from the surrounding actively deforming mountain ranges until a channel breaks through one of the sides and flushes the inward-draining basin of its sedimentary content. The complex numerical models provide a detailed insight into the geometry and complex three-dimensional structures within and at the margins of an orogen, and how they can be affected by erosional processes at the surface.