Advanced materials with greater strength and stiffness enable the use of slender, higher-aspect ratio wings that are aerodynamically favorable but exhibit greater flexibility than conventional wings. Even at an early stage of the design process, it is important to model the effects of wing flexibility using aeroelastic analysis. While dynamic aeroelastic phenomena are often critical in the design of wings, especially in the transonic regime, our focus is often on static aeroelastic analysis, called aerostructural analysis. We utilize detailed structural models that can be used to accurately size the structure for strength and buckling constraints, to predict structural weight, and to compute aerostructural deflections. These detailed structural models often include sophisticated structural design parametrizations for advanced materials. As a result, the full aerostructural design space may have thousands of design variables. To handle these large design problems in an efficient manner, we use gradient-based design optimization methods with an efficient coupled adjoint implementation that can be used to evaluate the derivative with respect to thousands of design variables in a reasonable computational time.