A review is given of recent advances in the physical properties of matter that arise at ultrahigh pressures when solids are compressed and irreversibly heated by intense shock and rarefaction waves. Experiments have been carried in the proximity of a nuclear explosion, and also with chemical explosives employing geometric and gradient cumulation. High-speed diagnostic techniques and interpretations of dynamic experiments are described. Measurements of shock compressibility under pressures of tens, hundreds, and thousands of millions of atmospheres are presented. Part I analyzes theoretical models of highly compressed plasma and, in particular, the contribution of the discrete spectrum to its thermodynamics. A comparison is made with nonideal plasma models and the role of phase transitions and of quantum shell effects is analyzed. Part II discusses determinations of the velocity of rarefaction waves that provide information on the optical properties of hot condensed-state plasmas. Determinations of the thermodynamic and radiative properties of plasmas produced by adiabatic expansion of shock-compressed states have led to advances in the theoretically difficult near-critical region of metals in which strongly coupled plasmas are produced and there is a change in plasma statistics.