Mantle dynamics can strongly affect melting processes beneath spreading centers and volcanic arcs. A 2-D numerical model of the Tonga subduction zone, with the slab viscously coupled to the mantle beneath the brittle-ductile transition but faulted above, shows that induced corner flow may cause asymmetric melting at the Lau back-arc spreading center, 400 km away. The down-going slab also entrains the high-viscosity base of the overlying lithosphere, drawing hot, low-viscosity asthenosphere upwards into the gap, triggering decompression melting in the wedge. Because the slab is decoupled from the brittle overlying plate, a cold upper corner develops, inhibiting melting where the slab is shallow. The cold corner is consistent with seismic attenuation and heat flow at arcs. Decompression melting may be a substantial fraction of magma production at some arcs, but less at others. Possibly more important, the shallow decompression melting structure may govern the pathways of melt extraction beneath volcanic arcs.