Over the past two decades or so, there have been many advances in the numerical simulation of hypersonic flows, with most effort focused on the development of upwind methods to produce accurate heat transfer rates for steady-state laminar and turbulent flows. With parallelizable implicit methods, it is now possible to obtain full-vehicle solutions at reasonable computational cost. This paper reviews several of the most widely used approaches and discusses how the methods have been tuned to control numerical errors for strongly shocked flows. The paper also discusses recent methods from the incompressible turbulence simulation literature that have been adapted to compressible flows. These methods have dramatically lower levels of numerical dissipation and have been extended to high-order accuracy on smoothly varying hexahedral grids. The increased accuracy of these methods enables the solution of complex physics unsteady hypersonic flows.