CRESST (Cryogenic Rare Event Search with Superconducting Thermometers) and the planned EURECA (European Underground Rare Event Calorimeter Array) are experiments aimed at the direct detection of Dark Matter. A well motivated candidate to account for Dark Matter are WIMPs (Weakly Interacting Massive Particles). The expected WIMP signature consists in a nuclear recoil of a few keV measured in low-temperature CaWO4 detectors equipped with superconducting transition sensors operated at a few mK. After a successful commissioning run in 2007 CRESST has presently taken more than 700 kilogram-days of Dark Matter data (2009-2011), which are presently under evaluation. A preliminary analysis of this data yields an excess of oxygen recoil events, which is presently difficult to explain with neutrons or alpha, beta and gamma background alone. If conventional background contributions can be ruled out, part of the signal could also be interpreted as a Dark Matter signature of low-mass WIMPs.