The frequency-domain analysis and synthesis of nonlinear systems are of fundamental importance in disciplines such as signal processing, mechanical engineering, and control engineering. However, these tasks are inherently challenging due to the complex nonlinear interactions and the implicit dependencies between system outputs and model parameters. Conventional methodologies—such as harmonic balance techniques and absolute stability theory—are frequently employed, yet they often encounter limitations stemming from computational intractability and analytical nonlinearity. To overcome these constraints, a generalized and systematic frequency-domain framework, termed the nonlinear characteristic output spectrum (nCOS) function,has been developed based on Volterra series theory. This approach enables a direct parametric characterization of nonlinear system behavior in the frequency domain, offering enhanced analytical tractability and interpretability. The nCOS methodology exhibits distinct advantages over traditional techniques, providing novel insights into the manifestation of nonlinear effects and facilitating the design of nonlinear dynamic systems. Extensive research has demonstrated the applicability of the nCOS framework across a range of engineering domains, including but not limited to vibration suppression, signal analysis, fault diagnostics, and structural optimization. This chapter presents a comprehensive and up-to-date review of recent advancements in the development and application of the nCOS method.