This paper provides an extensive documentation of applications of finite-dimensional nonlinear complementarity problems in engineering and equilibrium modeling. It describes various applications, including structural mechanics, contact mechanics, traffic equilibrium, and economic equilibria. The goal is to summarize the essential applications of the nonlinear complementarity problem, provide a basis for continued research, and supply a collection of realistic complementarity problems for algorithmic experimentation. Complementarity problems are central to system equilibrium, such as supply and demand in economics and mechanical contact. They are also fundamental in constrained optimization, with the complementary slackness property in linear programming. The paper discusses various types of complementarity problems, including nonlinear, variational inequalities, vertical complementarity, and saddle-point problems. It also covers mathematical programs with equilibrium constraints and their applications in engineering design and economic planning. The paper presents several engineering applications, such as contact mechanics problems, structural mechanics problems, and traffic equilibrium problems. It describes how these problems can be formulated as complementarity problems and provides functional expressions for these formulations. The paper also discusses computational methods for solving complementarity problems, including Newton's method, path search methods, quadratic programming-based algorithms, and interior point methods. The paper highlights the importance of complementarity problems in various fields, including economics, engineering, and sciences. It emphasizes the need for robust and efficient algorithms to solve these problems, as well as the importance of linking these algorithms with mathematical programming modeling languages for practical applications. The paper also discusses the development of model libraries for complementarity problems and the challenges they pose for researchers and algorithm designers.This paper provides an extensive documentation of applications of finite-dimensional nonlinear complementarity problems in engineering and equilibrium modeling. It describes various applications, including structural mechanics, contact mechanics, traffic equilibrium, and economic equilibria. The goal is to summarize the essential applications of the nonlinear complementarity problem, provide a basis for continued research, and supply a collection of realistic complementarity problems for algorithmic experimentation. Complementarity problems are central to system equilibrium, such as supply and demand in economics and mechanical contact. They are also fundamental in constrained optimization, with the complementary slackness property in linear programming. The paper discusses various types of complementarity problems, including nonlinear, variational inequalities, vertical complementarity, and saddle-point problems. It also covers mathematical programs with equilibrium constraints and their applications in engineering design and economic planning. The paper presents several engineering applications, such as contact mechanics problems, structural mechanics problems, and traffic equilibrium problems. It describes how these problems can be formulated as complementarity problems and provides functional expressions for these formulations. The paper also discusses computational methods for solving complementarity problems, including Newton's method, path search methods, quadratic programming-based algorithms, and interior point methods. The paper highlights the importance of complementarity problems in various fields, including economics, engineering, and sciences. It emphasizes the need for robust and efficient algorithms to solve these problems, as well as the importance of linking these algorithms with mathematical programming modeling languages for practical applications. The paper also discusses the development of model libraries for complementarity problems and the challenges they pose for researchers and algorithm designers.