Spectral element methods based on Hermite interpolation have a number of unique properties. First of all, the stabilization inherent in the interpolation process is sufficient to suppress nonlinear instabilities observed with other discretization schemes and leads to accurate linear transport of nonsmooth solutions. Second, and most important, they allow purely local time-stepping procedures limited only by geometric domain-of-dependence requirements. Thus high-order Hermite methods maximize the computation-to-communication ratio and therefore they admit highly efficient implementations on multicore processors. In this talk we focus on the application of Hermite methods to simulate unsteady compressible flows. Examples will include the direct simulation of the aeroacoustics of a low Reynolds number subsonic jet, as well as studies of more basic sound radiating flows. The latter will illustrate the coupling of Hermite methods with more standard discontinuous Galerkin discretizations to handle physical boundaries.