ABSTRACT:  We give an overview of discontinuous Galerkin (DG) methods for computational fluid dynamics (CFD). We discuss both matrix-based and matrix-free solution techniques and the pros and cons of both approaches. We introduce an optimal transport method for shock capturing and mesh adaptation of compressible flows.  We present extensive numerical results to demonstrate DG methods for a wide range of transonic, supersonic, hypersonic CFD problems including large eddy simulations of transonic and hypersonic turbulent flows on GPUs.