This paper provides a comprehensive documentation of finite-dimensional nonlinear complementarity problems (NCPs) in engineering and equilibrium modeling. The authors aim to summarize known applications, provide a basis for further research, and offer a collection of realistic problems for algorithmic experimentation. NCPs are prevalent in engineering and economics because they capture the concept of system equilibrium, such as the balance of supply and demand in economic systems. The paper discusses various types of NCPs, including nonlinear, variational, mixed, vertical, and saddle-point problems, and their formulations. It also covers the development of robust and efficient algorithms for solving these problems, emphasizing the importance of integrating algorithms with mathematical programming modeling languages like GAMS and AMPL. The paper includes detailed descriptions of engineering applications, such as contact mechanics, structural mechanics, and traffic equilibrium, along with their complementarity formulations. The goal is to highlight the pervasive nature of complementarity in these fields and to provide a valuable resource for researchers and practitioners.This paper provides a comprehensive documentation of finite-dimensional nonlinear complementarity problems (NCPs) in engineering and equilibrium modeling. The authors aim to summarize known applications, provide a basis for further research, and offer a collection of realistic problems for algorithmic experimentation. NCPs are prevalent in engineering and economics because they capture the concept of system equilibrium, such as the balance of supply and demand in economic systems. The paper discusses various types of NCPs, including nonlinear, variational, mixed, vertical, and saddle-point problems, and their formulations. It also covers the development of robust and efficient algorithms for solving these problems, emphasizing the importance of integrating algorithms with mathematical programming modeling languages like GAMS and AMPL. The paper includes detailed descriptions of engineering applications, such as contact mechanics, structural mechanics, and traffic equilibrium, along with their complementarity formulations. The goal is to highlight the pervasive nature of complementarity in these fields and to provide a valuable resource for researchers and practitioners.