Over the past two decades, surrogate modeling has received much attention from the researchers in the area of aerospace science and engineering due to its capability of greatly improving the efficiency of design optimization when high-fidelity numerical analysis is employed. Design optimization via surrogate models is intensively researched and eventually leads to a new type of optimization algorithm which is called surrogate-based optimization (SBO). Among the available surrogate models, such as polynomial response surface model, radial-basis functions, artificial neutral network, support-vector regression, multivariate interpolation or regression, and polynomial chaos expansion, Kriging model is the most representative surrogate model which has great potential in engineering design and optimization. In the context of aircraft design, this paper reviews the theory, algorithm and recent progress for researches on the Kriging surrogate model. First, the fundamental theory and algorithm of Kriging model are briefly reviewed and the experience about how to improve the robustness and efficiency is presented. Second, three major breakthroughs of Kriging model in recent years are reviewed, including gradient-enhanced Kriging, CoKriging and hierarchical Kriging. Third, the optimization mechanism and framework of surrogate-based optimization using Kriging model are discussed. In the meanwhile, the concept of infill-sampling criterion and sub optimization is presented. Five infill-sampling criteria as well as the dedicated constraint handling methods are described. Furthermore, the newly developed local EI (expected improvement) method and termination criteria for SBO are introduced. Fourth, a number of test cases including benchmark optimization problems as well as aerodynamic and multidisciplinary design optimization problems are given to demonstrate the excellent performance and great potential of the surrogate-based optimization using Kriging model. At last, the key challenges as well as future directions about the theory, algorithm and applications are discussed.