Recent advances in surrogate-based optimization focus on improving the efficiency and accuracy of design optimization through the use of surrogate models. These models approximate complex computational simulations, enabling faster evaluation of design alternatives. The paper reviews various surrogate modeling techniques, including polynomials, moving least-squares, radial basis functions, and Kriging, along with their applications in optimization strategies. It emphasizes the importance of selecting appropriate models based on the problem's characteristics and the need for careful sampling and validation. Surrogate models are built by first defining the design variables and selecting a sampling plan. Techniques like space-filling Latin hypercube sampling are used to ensure a uniform distribution of sample points. The choice of model depends on the nature of the problem, with polynomial models being widely used for their simplicity, while more complex methods like Kriging offer better accuracy in certain scenarios. Cross-validation is a key technique for assessing model performance and ensuring generalization. Polynomial models are evaluated using cross-validation to determine the optimal order, while Kriging models benefit from error estimation to improve prediction accuracy. Radial basis functions and support vector regression are also discussed, with the latter offering flexibility in handling noisy data. The paper highlights the importance of infill criteria in surrogate-based optimization, balancing exploration and exploitation of the design space. It also addresses the challenges of incorporating constraints and multiple objectives into the optimization process. Overall, the review underscores the need for careful model selection, validation, and adaptation to achieve effective surrogate-based optimization in aerospace and other engineering applications.Recent advances in surrogate-based optimization focus on improving the efficiency and accuracy of design optimization through the use of surrogate models. These models approximate complex computational simulations, enabling faster evaluation of design alternatives. The paper reviews various surrogate modeling techniques, including polynomials, moving least-squares, radial basis functions, and Kriging, along with their applications in optimization strategies. It emphasizes the importance of selecting appropriate models based on the problem's characteristics and the need for careful sampling and validation. Surrogate models are built by first defining the design variables and selecting a sampling plan. Techniques like space-filling Latin hypercube sampling are used to ensure a uniform distribution of sample points. The choice of model depends on the nature of the problem, with polynomial models being widely used for their simplicity, while more complex methods like Kriging offer better accuracy in certain scenarios. Cross-validation is a key technique for assessing model performance and ensuring generalization. Polynomial models are evaluated using cross-validation to determine the optimal order, while Kriging models benefit from error estimation to improve prediction accuracy. Radial basis functions and support vector regression are also discussed, with the latter offering flexibility in handling noisy data. The paper highlights the importance of infill criteria in surrogate-based optimization, balancing exploration and exploitation of the design space. It also addresses the challenges of incorporating constraints and multiple objectives into the optimization process. Overall, the review underscores the need for careful model selection, validation, and adaptation to achieve effective surrogate-based optimization in aerospace and other engineering applications.