This paper provides a comprehensive review of the past, present, and future developments in nonlinear system identification for structural dynamics. It highlights the fundamental differences between linear and nonlinear oscillations, emphasizing the challenges and unique features of nonlinear systems. The authors discuss various approaches to nonlinear system identification, including modal analysis for linear systems, and explore the limitations and assets of these methods in the context of nonlinear dynamics. The paper also delves into the concept of nonlinear normal modes (NNMs) and their role in understanding and modeling complex nonlinear behaviors. Additionally, it addresses the importance of experimental testing and system identification in reconciling numerical predictions with real-world observations. The authors identify future research directions, such as the development of more robust and accurate nonlinear system identification techniques, and the exploration of nonlinear phenomena like parametric resonance and nonlinear energy transfer. The paper concludes by discussing the scope and limitations of the review, noting that it focuses on areas where the authors have conducted research and does not cover all aspects of nonlinear dynamics.This paper provides a comprehensive review of the past, present, and future developments in nonlinear system identification for structural dynamics. It highlights the fundamental differences between linear and nonlinear oscillations, emphasizing the challenges and unique features of nonlinear systems. The authors discuss various approaches to nonlinear system identification, including modal analysis for linear systems, and explore the limitations and assets of these methods in the context of nonlinear dynamics. The paper also delves into the concept of nonlinear normal modes (NNMs) and their role in understanding and modeling complex nonlinear behaviors. Additionally, it addresses the importance of experimental testing and system identification in reconciling numerical predictions with real-world observations. The authors identify future research directions, such as the development of more robust and accurate nonlinear system identification techniques, and the exploration of nonlinear phenomena like parametric resonance and nonlinear energy transfer. The paper concludes by discussing the scope and limitations of the review, noting that it focuses on areas where the authors have conducted research and does not cover all aspects of nonlinear dynamics.