During the past several years, research teams around the world have developed astrophysics-relevant utilizing high energy-density facilities such as intense lasers and z-pinches. Research is underway in many areas, such as compressible hydrodynamic mixing, strong shock phenomena, radiation flow, radiative shocks and jets, complex opacities, equations of stat, and relativistic plasmas. Beyond this current research and the papers it is producing, plans are being made for the application, to astrophysics-relevant research, of the 2 MJ National Ignition Facility (NIF) laser at Lawrence Livermore National Laboratory; the 600 kj Ligne d'Intégration Laser (LIL) and the 2 MJ Laser Mégajoule (LMJ) in Bordeaux, France; petawatt-range lasers now under construction around the world; and current and future Z pinches. The goal of this conference and these proceedings is to continue focusing attention on this emerging research area. The conference brought together different scientists interested in this emerging new field, with topics covering: - Hydrodynamic instabilities in astrophysics, - Supernovae and supernova remnant evolution, - Astrophysical shocks, blast waves, and jets, - Stellar opacities, - Radiation and thermal transport, - Dense plasma atomic physics and EOS, - X-ray photoionized plasmas, - Ultrastrong magnetic field generation.