In the past decade, dual-phase xenon time projection chambers (Xe-TPCs) have emerged as some of the most powerful detectors in the fields of astroparticle physics and rare-event searches. Developed primarily towards the direct detection of dark matter particles, experiments presently operating deep underground have reached target masses at the multi-tonne scale, energy thresholds of approximately 1 keV and radioactivity-induced background rates similar to those from solar neutrinos. These unique properties, together with demonstrated stable operation over several years, allow for the exploration of new territory via high-sensitivity searches for a plethora of ultra-rare interactions. These include searches for particle dark matter, for second-order weak decays, and the observation of astrophysical neutrinos. We first review some properties of xenon as a radiation detection medium and the operation principles of dual-phase Xe-TPCs together with their energy calibration and resolution. We then discuss the status of currently running experiments and of proposed next-generation projects, describing some of the technological challenges. We end by looking at their sensitivity to dark matter candidates, to second-order weak decays and to solar and supernova neutrinos. Experiments based on dual-phase Xe-TPCs are difficult and, like all good experiments, they are constantly pushed to their limits. Together with many other endeavours in astroparticle physics and cosmology they will continue to push at the borders of the unknown, hopefully to reveal profound new knowledge about our cosmos. This article is part of the theme issue 'The particle-gravity frontier'.
Keywords: astrophysical neutrinos; dark matter direct detection; neutrinoless double-beta decay.