  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.
