Geophysicists have long sought direct, incontrovertible evidence from surface observables for convection in Earth's mantle. One of the best candidates for a phenomenon of convective origin is the South Pacific Superswell, a broad area of uplifted seafloor containing numerous volcanoes in French Polynesia. Other proposed examples of the superswell phenomenon include seafloor now located in the North Pacific that was anomalously shallow back in Cretaceous time and the present-day high topography of eastern and southern Africa. Researchers suggest that superswells form over mantle that is hotter than the global average on account of long-term absence of cooling by subducting lithosphere. Superswell mantle is melt rich, as evidenced by a fourfold increase in the rate of volcanism as compared with that of normal lithosphere. Seismic tomography suggests that the source for this diffuse, radiogenically enriched volcanism without long age progressions is a hot layer above the transition zone, rather than numerous deep-mantle plumes. Dynamic upwelling of this buoyant material in a low-viscosity zone immediately beneath the plate is responsible for both the shallow seafloor and the dip in the elevation of the Earth's sea level equipotential surface over French Polynesia. Thermal models consistent with the seismic tomography, depth, and geoid data predict extremely minor perturbations to the temperature structure in the upper 50 km of the lithosphere and thus unresolvable anomalies in both heat flow and the stiffness of the elastic plate supporting the volcanoes. Superswell volcanism is distinct from other types of volcanism by not being immediately attributable to plate separation, plate convergence, or deep-mantle plumes.