Abstract: CFD has been playing a more and more important role in aeronautics and astronautics as a critical tool of modern aircraft design and aerodynamics research. On the contrary, the improvement of key theories such as physical modelling and numerical scheme is developing slowly. Therefore, the paper focus on applications of CFD in aeronautics and astronautics from the perspectives of turbulence models, transition models, flux schemes and high order schemes, for which state-of-art achievements and challenges are discussed. For turbulence models, the development status and characteristics of the common linear viscosity models are reviewed with emphasis on their drawbacks. More complicated Reynolds stress models are also analyzed. For transition models, the low Reynolds number models, intermittency transition models and laminar kinetic energy models, focusing on the development, construction method and applicable scope of different models. For flux schemes, the upwind flux is mainly considered, reviewing the status of these methods for solving the problems of shock anomaly, overheating, all-speed simulation and multi-dimensional flow. For high order schemes, the WENO and DG methods are focused on, with review and comments on accuracy, temporal integration, shock capturing and costs. Finally, a brief conclusion and suggestions on future development are presented.