Status and perspectives of indirect and direct dark matter searches

In this review article the current status of particle dark matter is addressed. We discuss the main theoretical extensions of the standard model which allow to explain dark matter in terms of a (yet undiscovered) elementary particle. We then discuss the theoretical predictions for the searches of particle dark matter: direct detection in low-background underground experiments and indirect detection of neutrinos, gamma-rays and antimatter with terrestrial and space-borne detectors. Attention will be placed also on the discussion of the uncertainties, mainly of astrophysical origin, which affect the theoretical predictions. The constraints placed by these searches on the extensions of the standard models will be briefly addressed.