The recent WMAP data have confirmed that exotic dark matter together with the vacuum energy (cosmological constant) dominate in the flat Universe. Modern particle theories provide viable cold dark matter candidates with masses in the GeV-TeV region. All such candidates will be called WIMPs (Weakly Interacting Massive Particles). The nature of dark matter can only be unraveled by its direct detection in the laboratory. In this work we present some theoretical elements relevant to the direct dark matter detection experiments, paying particular attention to directional experiments, i.e. experiments in which not only the energy but the direction of the recoiling nucleus is observed. Since the direction of observation is fixed with respect to the Earth, while the Earth is rotating around its axis, in a directional experiment the angle between the direction of observation and the Sun’s direction of motion will change during the day. So, since the event rates sensitively depend on this angle, the observed signal in such experiments will exhibit very interesting and characteristic periodic diurnal variation.