Abstract
"Simulating physics with computers," Richard Feynman's keynote talk at the 1st conference on Physics and Computation (held at MIT in 1981), challenged scientists to harness quantum physics to simulate physical systems more efficiently than is achieved using classical physics, recognizing that the world around us is fundamentally quantum-mechanical. Today, programmable digital quantum computers are arising, promising realization of Feynman's vision. I review the algorithmic advances which are driving these promises, leavened by challenges still to be overcome.