With the advent of high-energy-density (HED) experimental facilities, such as high-energy lasers and fast Z-pinch pulsed-power facilities, millimeter-scale quantities of matter can be placed in extreme states of density, temperature, and/or velocity. With the commissioning of the NIF laser facility in the very near future, regimes experimentally accessible will be pushed to even higher densities and pressures. This is enabling the emergence of a new class of experimental science, wherein the properties of matter and the processes that occur under the most extreme physical conditions can be examined in the laboratory. Areas particularly suitable to laboratory astrophysics include the study of opacities relevant to stellar interiors, equations of state relevant to planetary interiors, strong shock-driven nonlinear hydrodynamics and radiative dynamics relevant to supernova explosions and subsequent evolution, protostellar jets and high Mach number flows, radiatively driven molecular clouds, nonlinear photoevaporation front dynamics, and photoionized plasmas relevant to accretion disks around compact objects such as black holes and neutron stars. In the area of materials science and condensed matter physics, material properties such as phase, elastic coefficients such as shear modulus, Peierls stress, and transport coefficients such as thermal diffusivity can be accessed at considerably higher densities and pressure than any existing data.