This paper reviews the past, present, and future of nonlinear system identification in structural dynamics. It discusses the differences between linear and nonlinear oscillations, the sources of nonlinearity in structural systems, and the challenges in identifying nonlinear systems. Nonlinearity is common in nature, and linear behavior is an exception. In structural dynamics, nonlinearities can arise from geometric, inertial, material, boundary condition, or external forces. Nonlinear system identification involves developing or improving structural models from experimental measurements. The paper highlights the importance of nonlinear system identification in engineering applications, where nonlinear behaviors can lead to unexpected and dangerous outcomes. It also discusses the challenges in identifying nonlinear systems, such as the lack of a general analysis method and the complexity of nonlinear dynamics. The paper emphasizes the need for future research in nonlinear system identification to improve the accuracy and reliability of structural models. It also discusses the importance of nonlinear system identification in verifying and validating structural models, and the need for further research to develop more effective methods for identifying nonlinear systems. The paper concludes that nonlinear system identification is a critical area of research in structural dynamics, with significant implications for engineering applications.This paper reviews the past, present, and future of nonlinear system identification in structural dynamics. It discusses the differences between linear and nonlinear oscillations, the sources of nonlinearity in structural systems, and the challenges in identifying nonlinear systems. Nonlinearity is common in nature, and linear behavior is an exception. In structural dynamics, nonlinearities can arise from geometric, inertial, material, boundary condition, or external forces. Nonlinear system identification involves developing or improving structural models from experimental measurements. The paper highlights the importance of nonlinear system identification in engineering applications, where nonlinear behaviors can lead to unexpected and dangerous outcomes. It also discusses the challenges in identifying nonlinear systems, such as the lack of a general analysis method and the complexity of nonlinear dynamics. The paper emphasizes the need for future research in nonlinear system identification to improve the accuracy and reliability of structural models. It also discusses the importance of nonlinear system identification in verifying and validating structural models, and the need for further research to develop more effective methods for identifying nonlinear systems. The paper concludes that nonlinear system identification is a critical area of research in structural dynamics, with significant implications for engineering applications.