The paper reviews the holographic correspondence between field theories and string/M theory, focusing on the relation between compactifications of string/M theory on Anti-de Sitter (AdS) spaces and conformal field theories (CFTs). It discusses the background, motivations, and evidence for this correspondence, emphasizing results derived in the regime where the field theory is approximated by classical or semiclassical gravity. The main example is the N=4 supersymmetric gauge theory in four dimensions, but the discussion also covers other dimensions, conformal and non-conformal, with or without supersymmetry, and its relation to quantum chromodynamics (QCD). The paper also discusses implications for black hole physics. The correspondence is derived from the physics of D3-branes in string theory, showing that the N=4 supersymmetric Yang-Mills theory is dual to string theory on AdS5 × S5. The correspondence is tested through matching the spectrum of chiral primary operators and correlation functions, and it provides an explicit holographic description of gravity. The paper also discusses other AdS backgrounds, D-branes, and deformations of the conformal field theory, as well as non-conformal and non-supersymmetric cases. It concludes that the AdS/CFT correspondence is a concrete realization of the holographic principle, where a gravitational theory in AdS is dual to a field theory on its boundary. The review highlights the importance of the large N limit in connecting gauge theories to string theories and the role of the holographic principle in quantum gravity.The paper reviews the holographic correspondence between field theories and string/M theory, focusing on the relation between compactifications of string/M theory on Anti-de Sitter (AdS) spaces and conformal field theories (CFTs). It discusses the background, motivations, and evidence for this correspondence, emphasizing results derived in the regime where the field theory is approximated by classical or semiclassical gravity. The main example is the N=4 supersymmetric gauge theory in four dimensions, but the discussion also covers other dimensions, conformal and non-conformal, with or without supersymmetry, and its relation to quantum chromodynamics (QCD). The paper also discusses implications for black hole physics. The correspondence is derived from the physics of D3-branes in string theory, showing that the N=4 supersymmetric Yang-Mills theory is dual to string theory on AdS5 × S5. The correspondence is tested through matching the spectrum of chiral primary operators and correlation functions, and it provides an explicit holographic description of gravity. The paper also discusses other AdS backgrounds, D-branes, and deformations of the conformal field theory, as well as non-conformal and non-supersymmetric cases. It concludes that the AdS/CFT correspondence is a concrete realization of the holographic principle, where a gravitational theory in AdS is dual to a field theory on its boundary. The review highlights the importance of the large N limit in connecting gauge theories to string theories and the role of the holographic principle in quantum gravity.