Based on the original combination of picosecond acoustics and diamond anvils cell, recent improvements to accurately measure hypersonic sound velocities of liquids and solids under extreme conditions are described. To illustrate the capability of this technique, results are given on the pressure and temperature dependence of acoustic properties for three prototypical cases: polycrystal (iron), single-crystal (silicon) and liquid (mercury) samples. It is shown that such technique also enables the determination of the density as a function of pressure for liquids, of the complete set of elastic constants for single crystals, and of the melting curve for any kind of material. High pressure ultrafast acoustic spectroscopy technique clearly opens opportunities to measure thermodynamical properties under previously unattainable extreme conditions. Beyond physics, this state-of-the-art experiment would thus be useful in many other fields such as nonlinear acoustics, oceanography, petrology, in of view. A brief description of new developments and future directions of works conclude the article. (C) 2014 Elsevier B.V. All rights reserved.