The XENON experiment aims at the direct detection of dark matter in the form of Weakly Interacting Massive Particles (WIMPs) via their elastic scattering off Xe nuclei. A fiducial mass of 1000 kg, distributed in 10 independent liquid xenon time projection chambers will be used to probe the lowest interaction cross-section predicted by SUSY models. The TPCs are operated in dual (liquid/gas) phase, to allow a measurement of nuclear recoils down to 16 keV energy, via simultaneous detection of the ionization, through secondary scintillation in the gas, and primary scintillation in the liquid. The distinct ratio of primary to secondary scintillation for nuclear recoils from WIMPs (or neutrons), and for electron recoils from background, is key to the event-by-event discrimination capability of XENON. A dual phase xenon prototype has been realized and is currently being tested, along with other prototypes dedicated to other measurements relevant to the XENON program. As part of the R&D phase, we will realize and move underground a first XENON module (XENON10) with at least 10 kg fiducial mass to measure the background rejection capability and to optimize the conditions for continuous and stable detector operation underground. We present some of the results from the on-going R&D and summarize the expected performance of the 10 kg experiment, from Monte-Carlo simulations. The main design features of the 100 kg detector unit(XENON100), with which we envisage to make up the 1 ton sensitive mass of XENON1T will also be presented.