In the EeV range, neutrinos are expected to be produced by ultra-high energy cosmic rays interactions with the Cosmic Microwave Background during propagation in the Universe. We report on the search for ultra-high energy neutrinos in data collected with the Surface Detector of the Pierre Auger Observatory. The searches are most efficient in the zenith angle range from 60 degrees to 95 degrees with tau neutrinos skimming in the Earth playingdominant role. The present non-detection of UHE neutrinos in the Pierre Auger Observatory excludes the most optimistic scenarios of neutrino production in terms of UHE cosmic rays chemical composition and cosmological evolution of the acceleration sites. We also report on the searches for neutrinos in coincidence with the recent Gravitational Wave events detected by LIGO/Virgo.