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Power density has grown to be the dominant challenge for continued complementary metal-oxide-semiconductor (CMOS) technology scaling. Together with recent improvements in microrelay design and process technology, this has led to renewed interest in mechanical computing for ultralow-power integrated circuit (IC) applications. This paper provides a brief history of mechanical computing followed by an overview of the various types of micromechanical switches, with particular emphasis on electromechanical relays since they are among the most promising for IC applications. Relay reliability and process integration challenges are discussed. Demonstrations of functional relay logic circuits are then presented, and relay scaling for improved device density and performance is described. Finally, the energy efficiency benefit of a scaled relay technology versus a CMOS technology with comparable minimum dimensions is assessed.