The fundamental particle nature of the Dark Matter (DM)that constitutes more than 80% of the gravitating matter inthe Universe is unknown. There is no suitable candidate forthis DM in the Standard Model (SM) of particle physics. Theso-called Weakly Interacting Massive Particles (WIMPs), predictedin many scenarios of possible new physics beyond theSM, are currently one of the most favoured candidates of theDM. A number of experiments worldwide are trying to directlydetect these WIMPs in underground laboratories. Herewe discuss the basic ideas behind the WIMP hypothesis andbriefly discuss the latest results of such experiments and futureprospects.