We study the sensitivity of large-scale xenon detectors to low-energy solar neutrinos, to coherent neutrino-nucleus scattering and to neutrinoless double beta decay. As a concrete example, we consider the xenon part of the proposed DARWIN (Dark Matter WIMP Search with Noble Liquids) experiment. We perform detailed Monte Carlo simulations of the expected backgrounds, considering realistic energy resolutions and thresholds in the detector. In a low-energy