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The DARPA COmpound semiconductor materials on silicon (COSMOS) program is developing processes to enable transistor-scale heterogeneous integration of advanced compound semiconductor (CS) devices with state of the art silicon circuits. The approaches to achieve this program goal include micro assembly, monolithic epitaxial growth, and epitaxy layer bonding processes. In Phase I of the program, performers have demonstrated high quality selective growth of CS materials on CMOS wafers, as well as successful heterogeneous integration of InP heterojunction bipolar transistors (HBT) with commercially fabricated complementary-metal-oxide- semiconductor (CMOS) transistors and demonstrated a fully functional heterogeneous differential amplifier circuit. This paper will review the program goals, discuss its implications, and present recent results.