Primordial backgrounds of relic gravitons

The diffuse backgrounds of relic gravitons with frequencies ranging between the aHz band and the GHz region encode the ultimate information on the primeval evolution of the plasma and on the underlying theory of gravity well before the electroweak epoch. While the temperature and polarization anisotropies of the microwave background radiation probe the low-frequency tail of the graviton spectra, during the next score year the pulsar timing arrays and the wide-band interferometers (both terrestrial and hopefully space-borne) will explore a much larger frequency window encompassing the nHz domain and the audio band. The salient theoretical aspects of the relic gravitons are reviewed in a cross-disciplinary perspective touching upon various unsettled questions of particle physics, cosmology and astrophysics.