The paper reviews recent advances in surrogate-based optimization methods, particularly in the context of aerospace design. It discusses the construction of surrogate models and their application in optimization strategies, emphasizing the importance of efficient global optimization. The authors cover various surrogate models, including polynomials, moving least-squares, radial basis functions (RBFs), Kriging, and support vector regression (SVR). Each method is described in detail, with a focus on its strengths and weaknesses. The paper also addresses key aspects such as cross-validation, model selection, and the handling of noisy data. The goal is to provide a comprehensive guide for practitioners and researchers interested in using surrogate-based methods for efficient and effective design optimization.The paper reviews recent advances in surrogate-based optimization methods, particularly in the context of aerospace design. It discusses the construction of surrogate models and their application in optimization strategies, emphasizing the importance of efficient global optimization. The authors cover various surrogate models, including polynomials, moving least-squares, radial basis functions (RBFs), Kriging, and support vector regression (SVR). Each method is described in detail, with a focus on its strengths and weaknesses. The paper also addresses key aspects such as cross-validation, model selection, and the handling of noisy data. The goal is to provide a comprehensive guide for practitioners and researchers interested in using surrogate-based methods for efficient and effective design optimization.