The fact that the mass of the visible stars could not account for the gravitational cohesion of the galaxy clusters was the first manifestation of non-radiating matter in the Universe. Since then, many observations imply that most of the matter is indeed dark. Its nature is still unknown and likely to have several contributions. Recent results indicate that most of it may not be composed of normal matter. These lectures will review the experimental methods which have been developed to unravel this 70-year long mystery and confront their results with the current theoretical framework of cosmology.