DARk matter WImp search with liquid xenoN (DARWIN) will be an experiment for the direct detection of dark matter using a multi-ton liquid xenon time projection chamber at its core. Its primary goal will be to explore the experimentally accessible parameter space for Weakly Interacting Massive Particles (WIMPs) in a wide mass-range, until neutrino interactions with the target become an irreducible background. The prompt scintillation light and the charge signals induced by particle interactions in the xenon will be observed by VUV sensitive, ultra-low background photosensors. Besides its excellent sensitivity to WIMPs above a mass of 5 GeV/c2, such a detector with its large mass, low-energy threshold and ultra-low background level will also be sensitive to other rare interactions. It will search for solar axions, galactic axion-like particles and the neutrinoless double-beta decay of 136Xe, as well as measure the low-energy solar neutrino flux with < 1% precision, observe coherent neutrino-nucleus interactions, and detect galactic supernovae. We present the concept of the DARWIN detector and discuss its physics reach, the main sources of backgrounds and the ongoing detector design and R&D efforts.