This paper provides a comprehensive overview of nonlinear black-box modeling in system identification, focusing on various approaches such as neural networks, radial basis functions, wavelet networks, and fuzzy models. It discusses the common features, choices, and considerations for successful system identification using these techniques. The authors highlight that nonlinear structures can be seen as a combination of two mappings: one from observed data to a regression vector and another from the regressor space to the output space. The paper covers the estimation techniques, including criterion minimization and two-step procedures, and addresses the challenge of handling a large number of parameters through regularization, shrinking, pruning, or regressor selection. It also reviews linear black-box models and their extensions, and discusses the properties of different basis functions, such as Fourier series, piecewise constant functions, and wavelets. The paper emphasizes the importance of selecting appropriate regressors and basis functions to achieve good model fit and discusses the trade-offs between bias and variance in model quality. Finally, it explores the flexibility of different model structures and the selection of relevant parameters to avoid overfitting.This paper provides a comprehensive overview of nonlinear black-box modeling in system identification, focusing on various approaches such as neural networks, radial basis functions, wavelet networks, and fuzzy models. It discusses the common features, choices, and considerations for successful system identification using these techniques. The authors highlight that nonlinear structures can be seen as a combination of two mappings: one from observed data to a regression vector and another from the regressor space to the output space. The paper covers the estimation techniques, including criterion minimization and two-step procedures, and addresses the challenge of handling a large number of parameters through regularization, shrinking, pruning, or regressor selection. It also reviews linear black-box models and their extensions, and discusses the properties of different basis functions, such as Fourier series, piecewise constant functions, and wavelets. The paper emphasizes the importance of selecting appropriate regressors and basis functions to achieve good model fit and discusses the trade-offs between bias and variance in model quality. Finally, it explores the flexibility of different model structures and the selection of relevant parameters to avoid overfitting.