An efficiency of 40.7% was measured and independently confirmed for a metamorphic three-junction GaInP∕GaInAs∕Ge cell under the standard spectrum for terrestrial concentrator solar cells at 240 suns (24.0W∕cm2, AM1.5D, low aerosol optical depth, 25°C). This is the initial demonstration of a solar cell with over 40% efficiency, and is the highest solar conversion efficiency yet achieved for any type of photovoltaic device. Lattice-matched concentrator cells have now reached 40.1% efficiency. Electron-hole recombination mechanisms are analyzed in metamorphic GaxIn1−xAs and GaxIn1−xP materials, and fundamental power losses are quantified to identify paths to still higher efficiencies.