High-efficiency Inverted Metamorphic (IMM) multi-junction solar cells are being developed at Spectrolab for use in space and near-space applications. Recently, large-area (26-cm2) IMM3J cells achieved a 1-sun, AM0 conversion efficiency of 32% with an open-circuit-voltage of 3.04 V, a short-circuit current-density of 16.7 mA/cm2, and a fill factor of 0.84. In addition, IMM4J cells (1-cm2) reached a 1-sun, AM0 conversion efficiency of 33%. The 4-junction cell achieved an open-circuit-voltage of 3.42 V, a short-circuit current-density of 15.8 mA/cm2, and a fill factor of 0.82. Both the inverted metamorphic 3J and 4J cells reveal excellent component subcell quantum efficiency. Improvements in crystal growth, as well as more optimal subcell current density balance, will further raise the 1-sun, AM0 efficiency of the 3J and the 4J IMM cells to 33% and 35% respectively. The latest status of the 72-cm2 XTJ (based on 150-mm Ge substrate) Supercells will also be discussed.