This talk will review some recent results on the structure of radiative shocks. Radiative shock waves have temperatures that are high enough (roughly on the order of one million Kelvin) that the effects of radiative photon transport must be included. These waves occur in high-energy density physics applications, such as in astrophysics and inertial confinement fusion. Similar to the shock structures that arise in gas kinetics (see Muller and Ruggeri, Rational Extended Thermodynamics, 1998, Springer), radiation transport introduces structure to hydrodynamic shock waves, even if the matter
is assumed to have a Maxwellian velocity distribution. For example, depending on the magnitude of the radiative effects and the shock
strength, the temperature distribution may be monotone or contain spikes, and the flow variables may be continuous or have a discontinuity. We will review the classic structure of hydrodynamics with heat conduction, which is a very simple of model of radiation
hydrodynamics. The effects of including more complicated nonequilibrium radiation models will then be illustrated through traveling-wave solutions to the governing radiation hydrodynamics system of equations. The challenges of numerical simulation will be
discussed, including results from a finite-volume computational physics code.