We have demonstrated world-record thermophotovoltaic (TPV) conversion efficiency in two materials systems operating at two different thermal emitter temperatures. A GaAs-based PV device under a 2330 °C thermal emitter produced an efficiency of (31 ± 2)%, and an In0.53Ga0.47As -based PV device under a 1300 °C thermal emitter produced an efficiency of (30 ± 2)%. The electrical output power densities of the cells were 2.45 W/cm2 and 0.658 W/cm2, respectively. Critical to these high efficiencies were the cells' high reflectance of photon energies below the absorber band gap. Unlike solar PV, for which sub-band gap (SBG) light is lost, a TPV cell can reflect SBG light back to the thermal emitter where it can be recycled. The demonstrations were made on a custom-built measurement platform in which a 100 cm2 graphite thermal emitter was heated under vacuum. The TPV efficiencies were evaluated by comparing the measured electrical output power of the cell with the total power absorbed by the cell. The measured TPV efficiencies as a function of thermal emitter temperature were corroborated by our full system modeling. As far as the authors are aware, these are the highest TPV conversion efficiencies ever measured, and device improvements should yield > 40% efficiency in the near future.