A combined h and p multigrid solution strategy is developed for high-order Discontinuous Galerkin dis-cretizations of the three-dimensional Euler equations. This solver is used to compute inviscid compressible flow over realistic three-dimensional aerodynamic configurations, and the performance of the solver in terms of convergence efficiency and parallel scalability is investigated. The hp multigrid solver is found to deliver nearly optimal convergence rates, which are insensitive to the discretization order p, and to the mesh resolu-tion h. The solver is also shown to scale well on massively parallel computer architectures, demonstrating good scalability up to 2008 processors of the NASA Columbia Supercomputer.