One of the great scientific enigmas still unsolved, the existence of dark matter, is reviewed. Simple gravitational arguments imply that most of the mass in the Universe, at least 90%, is some (unknown) non-luminous matter. Some particle candidates for dark matter are discussed with particular emphasis on the neutralino, a particle predicted by the supersymmetric extension of the Standard Model of particle physics. Experiments searching for these relic particles, carried out by many groups around the world, are also discussed. These experiments are becoming more sensitive every year and in fact one of the collaborations claims that the first direct evidence for dark matter has already been observed.