Abstract:The physical properties of hot dense matter over a broad domain of the phase diagram are of interest in astrophysics, planetary physics, power engineering, controlled thermonuclear fusion, impulse technologies, enginery, and other applications. The present report reviews the contribution of modern experimental methods and theories to the problem of the equation of state (EOS) at extreme conditions. Experimental techniques for high pressures and high energy density cumulation, the drivers of intense shock waves, and methods for the fast diagnostics of high-energy matter are considered. It is pointed out that the available high pressure and temperature information covers a broad range of the phase diagram, but only irregularly and, as a rule, is not thermodynamically complete; its generalization can be done only in the form of a thermodynamically complete EOS. As a practical example, construction of multi-phase EOS for tungsten is presented. The model's results are shown for numerous shock-wave data, the high-pressure melting and evaporation regions and the critical point of tungsten.