The paper discusses the surrogate-based analysis and optimization (SBAO) approach, which is crucial for addressing the competing objectives of improving performance, reducing costs, and enhancing safety in modern aerospace systems. SBAO involves constructing surrogates using data from high-fidelity models to provide fast approximations of objectives and constraints at new design points, making sensitivity and optimization studies feasible. The paper covers fundamental issues in SBAO, including the selection of loss functions and regularization criteria, design of experiments, surrogate selection and construction, sensitivity analysis, convergence, and optimization. It also presents a case study on the multi-objective optimal design of a liquid rocket injector to illustrate the state of the art and guide future efforts. Key topics include: 1. **Design of Experiments (DOE)**: Techniques such as Latin Hypercube Sampling (LHS), Orthogonal Arrays (OA), and optimal LHS are discussed, focusing on their uniformity and efficiency. 2. **Surrogate Model Construction**: Parametric (polynomial regression, Kriging) and non-parametric (radial basis functions, kernel-based regression) methods are explored, along with their estimation and appraisal components. 3. **Model Selection and Validation**: Approaches like Split Sample (SS), Cross Validation (CV), and Bootstrapping are reviewed for assessing the quality of surrogates. 4. **Sensitivity Analysis**: Methods such as the Morris Method, Iterated Fractional Factorial Design (IFFD), and Sobol's Method are discussed for understanding the impact of design variables on objectives. 5. **Surrogate-based Optimization**: The basic unconstrained SBAO algorithm and multiple surrogate-based optimization approaches are presented, along with techniques for ensuring convergence and handling non-linear constraints. The paper aims to provide a comprehensive overview of SBAO, emphasizing the concepts, methods, and practical implications, to guide researchers and practitioners in the field of aerospace engineering.The paper discusses the surrogate-based analysis and optimization (SBAO) approach, which is crucial for addressing the competing objectives of improving performance, reducing costs, and enhancing safety in modern aerospace systems. SBAO involves constructing surrogates using data from high-fidelity models to provide fast approximations of objectives and constraints at new design points, making sensitivity and optimization studies feasible. The paper covers fundamental issues in SBAO, including the selection of loss functions and regularization criteria, design of experiments, surrogate selection and construction, sensitivity analysis, convergence, and optimization. It also presents a case study on the multi-objective optimal design of a liquid rocket injector to illustrate the state of the art and guide future efforts. Key topics include: 1. **Design of Experiments (DOE)**: Techniques such as Latin Hypercube Sampling (LHS), Orthogonal Arrays (OA), and optimal LHS are discussed, focusing on their uniformity and efficiency. 2. **Surrogate Model Construction**: Parametric (polynomial regression, Kriging) and non-parametric (radial basis functions, kernel-based regression) methods are explored, along with their estimation and appraisal components. 3. **Model Selection and Validation**: Approaches like Split Sample (SS), Cross Validation (CV), and Bootstrapping are reviewed for assessing the quality of surrogates. 4. **Sensitivity Analysis**: Methods such as the Morris Method, Iterated Fractional Factorial Design (IFFD), and Sobol's Method are discussed for understanding the impact of design variables on objectives. 5. **Surrogate-based Optimization**: The basic unconstrained SBAO algorithm and multiple surrogate-based optimization approaches are presented, along with techniques for ensuring convergence and handling non-linear constraints. The paper aims to provide a comprehensive overview of SBAO, emphasizing the concepts, methods, and practical implications, to guide researchers and practitioners in the field of aerospace engineering.