Although first hints of the existence of Dark Matter were observed by the Swiss astronomer Zwicky already in the 1930s, only in recent years has it become known that the universe, in fact, is dominated by particles whose nature is almost unknown and which have never been directly observed. Meanwhile, as the existence of these particles is postulated not only by astronomy, but also cosmology and theoretical particle physics, there is significant effort to detect them in a laboratory experiment and determine their physical properties. However, as the interaction rate between Dark Matter particles and ordinary matter is extremely low, detectors have to be extremely sensitive. Low temperature detectors have been available for more than a decade and have now reached the highest sensitivity for direct Dark Matter detection. In this article, we give a short overview of observational results that suggest the existence of Dark Matter particles and what physicists have learned so far about their properties. The main focus is on the experimental challenges and effort for their direct detection.