We review the holographic correspondence between field theories and string/M theory,
focusing on the relation between compactifications of string/M theory on Anti-de Sitter
spaces and conformal field theories. We review the background for this correspondence
and discuss its motivations and the evidence for its correctness. We describe the main
results that have been derived from the correspondence in the regime that the field
theory is approximated by classical or semiclassical gravity. We focus on the case of
the N = 4 supersymmetric gauge theory in four dimensions, but we discuss also field
theories in other dimensions, conformal and non-conformal, with or without supersymmetry,
and in particular the relation to QCD. We also discuss some implications for
black hole physics.