A possible explanation of dark matter is the existence of an unobserved massive particle. The mass range and the interaction rate with ordinary matter extend over several orders of magnitude. Different detector technologies will be required in order to reach the necessary sensitivity. The CRESST III experiment (Cryogenic Rare Event Search with Superconducting Thermometers) is best suited to explore the sub-GeV mass region. At CRESST III Dark matter is detected by elastic scatters off a atomic nuclei, which currently provides the best limit in the mass region below 1.8 GeV/c^2. Besides CRESST III a brief summary of dark matter search results using different approaches, like liquid nobel gas detectors, is presented.