We describe the role for the next-generation “superlasers” in the study of matter under extremely high-energy-density conditions in comparison with previous uses of nuclear explosives for this purpose. As examples, we focus on three important areas of physics that have unresolved issues that must be addressed by experiment: equations of state, hydrodynamic instabilities, and the transport of radiation. We describe some of the advantages the large lasers will have in a comprehensive, laboratory-based experimental program.