This chapter 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). The authors discuss the background, motivations, and evidence for this correspondence, emphasizing the case of the $\mathcal{N} = 4$ supersymmetric gauge theory in four dimensions. They also explore other dimensions, conformal and non-conformal field theories, and their relation to QCD. Additionally, they delve into implications for black hole physics, including the calculation of black hole entropy and the matching of chiral primary operators and correlation functions. The chapter is structured into several sections, covering topics such as large $N$ gauge theories, D-branes, and the AdS/CFT correspondence, providing a comprehensive overview of the subject.This chapter 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). The authors discuss the background, motivations, and evidence for this correspondence, emphasizing the case of the $\mathcal{N} = 4$ supersymmetric gauge theory in four dimensions. They also explore other dimensions, conformal and non-conformal field theories, and their relation to QCD. Additionally, they delve into implications for black hole physics, including the calculation of black hole entropy and the matching of chiral primary operators and correlation functions. The chapter is structured into several sections, covering topics such as large $N$ gauge theories, D-branes, and the AdS/CFT correspondence, providing a comprehensive overview of the subject.