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In past years, liquid rare gas detectors (LRGD) have made a considerable progress and found application in various fields of research, such as high energy experiments, astrophysics, search for rare processes and medical imaging. This review paper starts by a short summary and discussion of the properties of liquid rare gases (LRG) that make them attractive as radiation detector media. Next, the two best-established technologies based on liquid rare gases, electromagnetic calorimeters and time projection chambers, are briefly reviewed along with their main applications. The bulk of the paper is focused on the challenging development of LRGD for the search of rare processes in low background experiments with an emphasis on those dealing with the direct detection of dark matter. The challenges posed by those experiments, the detectors proposed and their present status of development are described. A brief review of the proposals of using LRGD for medical imaging is outlined and the present status of some of the more significant developments under way is presented.