ABSTRACT Recent advances in compact and readily fabricated magnetic thin film devices have created great interest for their application in magnetic memory technologies, in particular, racetrack memories. However, most work to date has been carried out using two‐dimensional racetracks but the full potential of racetrack memory can only be achieved with three‐dimensional architectures. A range of 3D geometries can significantly influence magnetic interactions through spatial curvature. In this work, we investigate nanoribbons with curvilinear surfaces onto which Pt/Co/Ni/Co multilayers are formed by sputter deposition techniques and the consequent current‐induced domain wall dynamics. Nanoribbons with controllable cross‐sectional curvatures are formed by advanced multiphoton lithography. We show that the surface curvature, whether concave or convex, can either enhance or suppress the current‐induced domain wall motion. These different responses arise from Oersted fields generated by the current flowing through these curvilinear geometries. In these structures, up‐down and down‐up domain walls move at the same velocity under current injection. However, by introducing more complex hybrid structures that incorporate both concave and convex sections across the nanoribbon's width, we show that up‐down and down‐up domain walls have distinct velocities, and consequently can act as a domain wall filter.