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A stochastic background of gravitational waves can be described as a superposition of several uncorrelated contributions. It can be of both cosmological and astrophysical origin. In the first case, it can constitute potentially a unique probe of the primordial universe. In the second, it can give precious information on stellar populations. After discussing how this kind of signal can be detected and what information can be extracted from its study, I review the past and ongoing efforts to find it, the current upper limits and the future perspective for its detection.

Stochastic GW searches and Cosmology with GWs