Summary: This article reviews the plane-wave/super Yang-Mills duality, which states that strings on a plane-wave background are dual to a particular large \(R\)-charge sector of \(\mathcal N=4\), \(D=4\) superconformal \(U(N)\) gauge theory. This duality is a specification of the usual anti-de Sitter/conformed field theory (AdS/CFT) correspondence in the “Penrose limit.” The Penrose limit of \(\text{AdS}_5\times S^5\) leads to the maximally supersymmetric ten-dimensional plane wave (henceforth “the” plane wave) and corresponds to restricting to the large \(R\)-charge sector, the Berenstein-Maldacena-Nastase (BMN) sector, of the dual superconformal field theory. After reviewing the necessary background, the authors state the duality and review some of its supporting evidence. They discuss the suggestion by ’t Hooft that Yang-Mills theories with gauge groups of large rank might be dual to string theories and the realization of this conjecture in the form of the AdS/CFT duality. Plane waves as exact solutions of supergravity and their appearance as Penrose limits of other backgrounds are considered, followed by an overview of string theory on the plane-wave background, discussing the symmetries and spectrum. The article then makes precise the statement of the proposed duality and classifies the BMN operators. It examines the gauge theory side of the duality, studying both quantum and nonplanar corrections to correlation functions of BMN operators and their operator-product expansions. The important issue of operator mixing and the resultant need for rediagonalization is stressed. Finally, the article studies strings on the plane wave via light-cone string field theory and demonstrates agreement between the one-loop correction to the string mass spectrum and the corresponding quantity in the gauge theory. A new presentation of the relevant superalgebra is given.