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We have been developing a phaseless auxiliary-field quantum Monte Carlo (AFQMC) method for ground- and excited-state calculations of electronic systems. This is an orbital-based many-body approach applicable with any single-particle basis. It takes the form of parallel streams of random walks, each of which resembles a density-functional theory (DFT) calculation in a fluctuating external potential. The fermion sign/phase problem is often significantly reduced in this framework. We formulate an approximate constraint on the random walk paths to control the sign/phase problem. In about 100 molecular and solid systems tested to date, the method has given results at or near
chemical accuracy. The phaseless AFQMC method scales as M^3-M^4 with basis size M. I will discuss the conceptual framework, and illustrate with a few recent applications: the Hubbard model, pressure-induced transition from diamond to beta-tin in silicon, and
excited states in molecules.
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