  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.
