[en] The application of high-power pulsed lasers to ultrahigh pressure equation-of-state (EOS) experiments is discussed. It is shown that pressures along the principal Hugoniot between 1 and 10 TPa can be produced with existing lasers used for inertial-confinement fusion research. The relevance of measurements in this pressure regime to improving our understanding of condensed matter physics is also discussed. New experimental techniques as well as potential experimental problems are described, and EOS experiments on the Janus and Argus laser systems are proposed