In this article we describe recent progress in the computational many-body theory of metal surfaces, and focus on current techniques beyond the local-density approximation of density-functional theory. We overview various applications to ground and excited states. We discuss the exchange-correlation hole, the surface energy, and the work function of jellium surfaces, as obtained within the random-phase approximation, a time-dependent density-functional approach, and quantum Monte Carlo methods. We also present a survey of recent quasiparticle calculations of unoccupied states at both jellium and real surfaces.

17 pages, 1 figure, to appear in Comput. Phys. Commun