Abstract: Unlike the relic photons, relic neutrinos have not so far been observed. The Cosmic Neutrino Background  is the oldest relic from the Big Bang, produced a few seconds after the Bang itself. Due to their impact in cosmology, relic neutrinos may be revealed indireclty in the near future through cosmological observations. In this talk we concentrate on other proposals, made in the last 30 years, to try to detect the Cosmic Neutrino Background  directly, either in laboratory searches (through tiny
accelerations they produce on macroscopic targets) or through astrophysical observations (looking for absorption dips in the flux of Ultra-High Energy neutrinos, due to the annihilation of these neutrinos with relic neutrinos at the Z-resonance). We concentrate mainly on the first of these two possibilities.