This article reviews the progress made over the last 20 years in the development and applications of liquid xenon detectors in particle physics, astrophysics and medical imaging experiments. We begin with a summary of the fundamental properties of liquid xenon as radiation detection medium, in light of the most current theoretical and experimental information. After a brief introduction of the different type of liquid xenon detectors, we continue with a review of past, current and future experiments using liquid xenon to search for rare processes and to image radiation in space and in medicine. We will introduce each application with a brief survey of the underlying scientific motivation and experimental requirements, before reviewing the basic characteristics and expected performance of each experiment. Within this decade it appears likely that large volume liquid xenon detectors operated in different modes will contribute to answering some of the most fundamental questions in particle physics, astrophysics and cosmology, fulfilling the most demanding detection challenges. From experiments like MEG, currently the largest liquid xenon scintillation detector in operation, dedicated to the rare mu -> e + gamma decay, to the future XMASS which also exploits only liquid xenon scintillation to address an ambitious program of rare event searches, to the class of time projection chambers like XENON and EXO which exploit both scintillation and ionization of liquid xenon for dark matter and neutrinoless double beta decay, respectively, we anticipate unrivaled performance and important contributions to physics in the next few years.
