Neutrinos with energies above 100 PeV are detectable with the Surface Detector array (SD) of the Pierre Auger Observatory. Identification is efficiently done for neutrinos of all flavors interacting in the atmosphere at large zenith angles (downward-going DG), as well as for Earth-skimming (ES) tau neutrinos. No neutrino candidates were found up to 31 August 2018, and this allowed us to put upper bounds on their flux that constrain several models of cosmic-ray and neutrino production at EeV energies. With the SD of Auger we can also search for neutrinos from point-like sources, monitoring a large fraction of the sky (from $\sim -80^\circ$ to $\sim +60^\circ$) in equatorial declination with peak sensitivities at declinations around $-53^\circ$ and $+55^\circ$, unmatched in the northern hemisphere. An excellent sensitivity can also be obtained in the case of transient sources lasting of order an hour or less if they occur when the source is in the field of view of the ES or DG channels.