Astrophysical backgrounds of gravitational waves: an overview

The astrophysical background of gravitational waves (AGWB) is composed by the incoherent superposition of gravitational wave signals emitted by resolved and unresolved astrophysical sources from the onset of stellar activity until today. In this talk, I  will present a theoretical framework  to characterize the AGWB in terms of energy density and polarization and  I will show predictions for the angular power spectra of the background anisotropy and for its cross-correlations with electromagnetic observables, in the frequency bands accessible by  LIGO/Virgo and  LISA.  I will then discuss the astrophysical content of these observables, give an overview of the state of the art of observations, and highlight future observational challenges.