The high efficiency of multijunction concentrator cells has the potential to revolutionize the cost structure of photovoltaic electricity generation. Advances in the design of metamorphic subcells to reduce carrier recombination and increase voltage, wide-band-gap tunnel junctions capable of operating at high concentration, metamorphic buffers to transition from the substrate lattice constant to that of the epitaxial subcells, concentrator cell AR coating and grid design, and integration into 3-junction cells with current-matched subcells under the terrestrial spectrum have resulted in new heights in solar cell performance. A metamorphic Ga0.44In0.56P/Ga0.92In0.08As/ Ge 3-junction solar cell from this research has reached a record 40.7% efficiency at 240 suns, under the standard reporting spectrum for terrestrial concentrator cells (AM1.5 direct, low-AOD, 24.0 W/cm2, 25∘C), and experimental lattice-matched 3-junction cells have now also achieved over 40% efficiency, with 40.1% measured at 135 suns. This metamorphic 3-junction device is the first solar cell to reach over 40% in efficiency, and has the highest solar conversion efficiency for any type of photovoltaic cell developed to date. Solar cells with more junctions offer the potential for still higher efficiencies to be reached. Four-junction cells limited by radiative recombination can reach over 58% in principle, and practical 4-junction cell efficiencies over 46% are possible with the right combination of band gaps, taking into account series resistance and gridline shadowing. Many of the optimum band gaps for maximum energy conversion can be accessed with metamorphic semiconductor materials. The lower current in cells with 4 or more junctions, resulting in lower I2R resistive power loss, is a particularly significant advantage in concentrator PV systems. Prototype 4-junction terrestrial concentrator cells have been grown by metal-organic vapor-phase epitaxy, with preliminary measured efficiency of 35.7% under the AM1.5 direct terrestrial solar spectrum at 256 suns.