Most of the matter in the Universe is not in the form of known atoms, but is made from some new, unknown kind of matter. The nature of this so-called Dark Matter is one of the greatest outstanding questions of contemporary physics. As we fly with the Solar System through the Milky Way, we constantly plow through a halo of this Dark Matter. One way to unravel what Dark Matter is made of is to try to detect some of these particles as they pass through a detector on Earth. I will review the design principles and performance of the XENON project, currently operating the most sensitive detector to search for such Dark Matter particles. XENON100 uses ultra-pure liquid xenon in a cryostat made from carefully selected materials to reduce the radioactive background from known particles. It is located about a mile deep underground in the Laboratori Nazionali del Gran Sasso in central Italy to shield it from cosmic radiation, and behind a thick shield of lead and other materials to shield other ambient radioactivity. The liquid xenon is equipped with photomultipliers in a so-called Time Projection Chamber so that each particle interaction can be localized in three dimensions. This helps to further reduce radioactive backgrounds, which are mostly located near the surfaces, from Dark Matter interactions, which are expected to occur throughout the target volume. Furthermore, radioactive beta- and gamma-radiation can be distinguished from neutrons or Dark Matter events based on the light and charge signal that is left by each interaction.  XENON100 has already placed the most stringent constraints on the properties of Dark matter particles and new data are about to be released. At the same time the next phase of the XENON program with a ton scale detector (XENON1T) is advancing rapidly.