The CRESST-III experiment (Cryogenic Rare Events Search with Superconducting Thermometers), located at the underground facility Laboratori Nazionali del Gran Sasso in Italy, uses scintillating CaWO_4 crystals as cryogenic calorimeters to search for direct dark matter interactions in detectors. A large part of the parameter space for spin-independent scattering off nuclei remains untested for dark matter particles with masses below a few GeV/c^2, despite many naturally motivated theoretical models for light dark matter particles. The CRESST-III detectors are designed to achieve the performance required to probe the low-mass region of the parameter space with a sensitivity never reached before. In this paper, new results on the performance and an overview of the CRESST-III detectors will be presented, emphasizing the results about the low-energy threshold for nuclear recoil of CRESST-III Phase 1 which started collecting data in August 2016.
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