Computational aeroelasticity is a dynamic area of research relevant to a wide range of aerospace systems and problems. In this presentation, an overview of research challenges associated with computational aeroelasticity will be provided through demonstrations of various test cases. The focus of the presentation is to illustrate problems that might be encountered by a researcher who is active in computational aeroelasticity, including time synchronization of separately run solvers and issues with turbulence modeling for separated flows around elastic configurations. Recent progress in extending aeroleastic modeling from a modal-based approach to fully coupled non-modal based approach will be outlined.