Nowadays there is strong evidence that a large fraction of the matter in the universe is of a yet unknown type, which is usually called dark matter (DM). It is not composed of quarks and also not interacting electromagnetically. The CRESST dark matter search is looking for signatures of these DM particles by calorimetrically measuring the recoil energies of particles hitting an array of well shielded CaWO4 crystals with ~10 kg combined mass at operating temperatures of a few mK. Electromagnetically interacting particles are discriminated by simultaneously measuring the produced scintillation light for each recoil. As the current upper limits for the DM-to-normal matter interaction cross section are on the level of 8 • 10−46 cm2, large targe...