ESPRESSO, the Echelle SPectrograph for Rocky Exoplanets and Stable Spectroscopic Observations, will combine the efficiency of modern echelle spectrograph design with extreme radial-velocity precision. It will be installed on ESO's VLT in order to achieve a gain of two magnitudes with respect to its predecessor HARPS, and the instrumental radialvelocity precision will be improved to reach cm/s level. Thanks to its characteristics and the ability of combining incoherently the light of 4 large telescopes, ESPRESSO will offer new possibilities in various fields of astronomy. The main scientific objectives will be the search and characterization of rocky exoplanets in the habitable zone of quiet, nearby G to M-dwarfs, and the analysis of the variability of fundamental physical constants. We will present the ambitious scientific objectives, the capabilities of ESPRESSO, and the technical solutions of this challenging project.