Aerodynamic shape optimization is powerful in automating aircraft design and enhancing design performance. Despite its potential advantages, there are several challenging issues that require more advanced solutions, including robust design, fast interactive design, and design optimization with discontinuous aerodynamic functions. These challenges are primarily caused by the high dimensionality of aerodynamic shapes and the high cost of computational fluid dynamics. In this seminar, we will present our recent research in tackling these fundamental issues using machine learning. We will also discuss the benefits that these approaches in aerodynamic design optimization of airfoils, wings, and aircraft.