Geodetic and paleogeodetic measurements of interseismic strain above the Sumatran portion of the Sunda subduction zone reveal a heterogeneous pattern of coupling. Annual banding in corals provides vertical rates of deformation spanning the last half of the 20th century, and repeated GPS surveys between 1991 and 2001 and continuous measurements at GPS stations operated since 2002 provide horizontal velocities. Near the equator, the megathrust is locked over a narrow width of only a few tens of kilometers. In contrast, the locked fault zone is up to about 175 km wide in areas where great interplate earthquakes have occurred in the past. Formal inversion of the data reveals that these strongly coupled patches are roughly coincident with asperities that ruptured during these events. The correlation is most spectacular for rupture of the Mw 8.7 Nias-Simeulue earthquake of 2005, which released half of the moment deficit that had accumulated since its previous rupture in 1861, suggesting that this earthquake was overdue. Beneath the Mentawai islands, strong coupling is observed within the overlapping rupture areas of the great earthquakes of 1797 and 1833. The accumulated slip deficit since these events is slowly reaching the amount of slip that occurred during the 1833 earthquake but already exceeds the slip that occurred during the 1797 earthquake. Thus, rerupture of part of the Mentawai patch in September 2007 was not a surprise. In contrast, coupling is low below the Batu islands near the equator and around Enggano island at about 5°S, where only moderate earthquakes (Mw < 8.0) have occurred in the past two centuries. The correlation of large seismic asperities with patches that are locked during the interseismic period suggests that they are persistent features. This interpretation is reinforced by the fact that the large locked patches and great ruptures occur beneath persistent geomorphologic features, the largest outer arc islands. Depth- and convergence-rate-dependent temperature might influence the pattern of coupling, through its effect on the rheology of the plate interface, but other influences are required to account for the observed along-strike heterogeneity of coupling. In particular, subduction of the Investigator Fracture Zone could be the cause for the low coupling near the equator.