The selective catalytic reduction (SCR) of NO x compounds with NH 3 is a hot topic in recent years. Among various catalysts, zeolites are proved to be efficient and promising for NH 3 -SCR, yet the whole processes and intrinsic mechanism are still not well understood due to the structural complexity of zeolites. With the improvement of theoretical chemistry techniques, quantum-chemical calculations are now capable of modeling the structure, acidity, adsorption, and ultimately reaction pathways over zeolites to some extent. In this review, a brief summary of relevant concepts of NH 3 -SCR is presented. Cluster approaches, embedded techniques, and periodic treatments are described as three main methods. Details of quantum-chemical investigations toward the key issues such as, the structure of active sites, the adsorption of small molecules, and the reaction mechanism of NH 3 -SCR over zeolites are discussed. Finally, a perspective for future theoretical research is given. V C 2014 Wiley Periodicals, Inc.