High compression is usually attained through several laser-driven shocks or continuous compression. The propagation of such strong shocks depends on the material equation of state (the EOS is another equation of radiative hydrodynamics). The EOS of most materials is not well known in the Mbar and gigabar range of pressure. A better determination of the EOS at such high pressures also has important applications in astrophysics as to the understanding of the dynamic behavior of the cores of stars and planets. Until recently, EOS data could be obtained only through underground nuclear explosions. Using high-power lasers, we are now able to collect important information on the equation of state of many materials in the high-energy-density regime. The laws of radiative hydrodynamics describe the compression of matter into the parameter space of high-energy-density physics. At full compression, the plasma pressure in an ICF capsule is of the order of billions of bars. The high temperature and high densities trigger the thermonuclear ignition and propagating burn wave. To study the ignition process, the equations of radiative hydrodynamics must be improved by including models of nuclear reaction rates and alpha-particle energy deposition in the core of the compressed capsule. At the Laboratory for Laser Energetics, full two-dimensional simulations of the implosion, ignition, and burn of a DT capsule are routinely performed to determine the optimum design of the high-gain target to be used in the National Ignition Facility. Faculty in Mechanical Engineering and Physics are actively involved in the study of radiative hydrodynamics and hydrodynamic instability in inertial confinement fusion and astrophysics.