Subducting slabs provide the main driving force for plate motion and flow in the Earth's mantle, and geodynamic, seismic and geochemical studies offer insight into slab dynamics and subduction-induced flow. Most previous geodynamic studies treat subduction zones as either infinite in trench-parallel extent (that is, two-dimensional) or finite in width but fixed in space. Subduction zones and their associated slabs are, however, limited in lateral extent (250-7,400 km) and their three-dimensional geometry evolves over time. Here we show that slab width controls two first-order features of plate tectonics-the curvature of subduction zones and their tendency to retreat backwards with time. Using three-dimensional numerical simulations of free subduction, we show that trench migration rate is inversely related to slab width and depends on proximity to a lateral slab edge. These results are consistent with retreat velocities observed globally, with maximum velocities (6-16 cm yr-1) only observed close to slab edges (<1,200 km), whereas far from edges (>2,000 km) retreat velocities are always slow (<2.0 cm yr-1). Models with narrow slabs (≤1,500 km) retreat fast and develop a curved geometry, concave towards the mantle wedge side. Models with slabs intermediate in width (∼2,000-3,000 km) are sublinear and retreat more slowly. Models with wide slabs (≥4,000 km) are nearly stationary in the centre and develop a convex geometry, whereas trench retreat increases towards concave-shaped edges. Additionally, we identify periods (5-10 Myr) of slow trench advance at the centre of wide slabs. Such wide-slab behaviour may explain mountain building in the central Andes, as being a consequence of its tectonic setting, far from slab edges.