Finding a solution to the Dark Matter problem is surely one of the main challenges of modern cosmology. The existence of both Dark Matter and Dark Energy has been formulated on the basis of strong observational evidences, and constitutes the main success of the most accredited cosmological models. Yet none of them has been directly detected. In this review the Dark Matter problem will be discussed and the approaches to directly detect it, in the form of a special category of particles, i.e. the WIMPs (Weakly Interacting Massive Particles), will be presented and discussed
