We study the Makran subduction zone, along the southern coasts of Iran and Pakistan, to gain insights into the kinematics and dynamics of accretionary prism deformation. By combining techniques from seismology, geodesy and geomorphology, we are able to put constraints on the shape of the subduction interface and the style of strain across the prism. We also address the long-standing tectonic problem of how the right-lateral shear taken up by strike-slip faulting in the Sistan Suture Zone in eastern Iran is accommodated at the zone's southern end. We find that the subduction interface in the western Makran may be locked, accumulating elastic strain, and move in megathrust earthquakes. Such earthquakes, and associated tsunamis, present a significant hazard to populations around the Arabian Sea.