Oceanic arcs and deep-sea trenches are the surface expressions of oceanic plates subducting into the Earth's mantle. We use a new numerical technique for simulating the dynamical evolution of the lithosphere-mantle interaction in order to assess the causes of arc curvature. We group the possible causes into two classes, external feedback between the migrating lithosphere and the secondary induced mantle flow, and internal heterogeneities within the lithosphere, e.g., owing to differences in cooling ages of the plate at the trench. We statistically assess that almost all arcs on the Earth can be described by these hypotheses. The method is also directly applied to the Tonga and Aleutian arcs, bringing new insights on the origin of their shapes.