Astrophysical sources emit gravitational waves in a large variety of processes occurred since the beginning of star and galaxy formation. These waves permeate our high redshift Universe, and form a background which is the result of the superposition of different components, each associated to a specific astrophysical process. Each component has different spectral properties and features that it is important to investigate in view of a possible, future detection. In this contribution, we will review recent theoretical predictions for backgrounds produced by extragalactic sources and discuss their detectability with current and future gravitational wave observatories.
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