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CRESST-III, the third generation of CRESST, was specifically designed to have a world-leading sensitivity for low-mass dark matter (DM) (less than 2\u00a0GeV\/$$\\hbox {c}^{2}$$<\/jats:tex-math>c<\/mml:mtext>2<\/mml:mn><\/mml:msup><\/mml:math><\/jats:alternatives><\/jats:inline-formula>) to probe the spin-independent DM-nucleus cross section. At present, a large part of the parameter space for spin-independent scattering off nuclei remains untested for dark matter particles with masses below few GeV\/$$\\hbox {c}^{2}$$<\/jats:tex-math>c<\/mml:mtext>2<\/mml:mn><\/mml:msup><\/mml:math><\/jats:alternatives><\/jats:inline-formula> although many motivated theoretical models having been proposed. The CRESST-III experiment employs scintillating $$\\hbox {CaWO}_{{4}}$$<\/jats:tex-math>CaWO<\/mml:mtext>4<\/mml:mn><\/mml:msub><\/mml:math><\/jats:alternatives><\/jats:inline-formula> crystals of $$\\sim$$<\/jats:tex-math>\u223c<\/mml:mo><\/mml:math><\/jats:alternatives><\/jats:inline-formula> 25\u00a0g as target material for dark matter interactions operated as cryogenic scintillating calorimeters at\u00a0$$\\sim$$<\/jats:tex-math>\u223c<\/mml:mo><\/mml:math><\/jats:alternatives><\/jats:inline-formula> 10\u00a0mK. CRESST-III first data taking was successfully completed in 2018, achieving an unprecedented energy threshold for nuclear recoils. This result extended the present sensitivity to DM particles as light as $$\\sim$$<\/jats:tex-math>\u223c<\/mml:mo><\/mml:math><\/jats:alternatives><\/jats:inline-formula> 160\u00a0MeV\/$$\\hbox {c}^{2}$$<\/jats:tex-math>c<\/mml:mtext>2<\/mml:mn><\/mml:msup><\/mml:math><\/jats:alternatives><\/jats:inline-formula>. In this paper, an overview of the CRESST-III detectors and results will be presented.<\/jats:p>","DOI":"10.1007\/s10909-020-02343-3","type":"journal-article","created":{"date-parts":[[2020,2,1]],"date-time":"2020-02-01T09:02:47Z","timestamp":1580547767000},"page":"547-555","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Searches for Light Dark Matter with the CRESST-III Experiment"],"prefix":"10.1007","volume":"199","author":[{"name":"The CRESST Collaboration","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9805-475X","authenticated-orcid":false,"given":"M.","family":"Mancuso","sequence":"first","affiliation":[]},{"given":"A. 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