The Pierre Auger Observatory is sensitive to ultra-high energy neutral particles, such as photons, neutrinos, and neutrons, and can take part in Multi-Messenger searches in collaboration with other observatories. Photons and neutrinos are searched by exploiting the design of the Pierre Auger Observatory and profiting from the different properties of the induced showers caused by different particles. Diffuse and point source fluxes of photons and neutrinos are searched for. Furthermore, photon and neutrino follow-ups of the gravitational wave events observed by the LIGO/Virgo Collaboration are conducted. The Pierre Auger Observatory is also used to search for neutrons from point-like sources. In contrast to photons and neutrinos, neutrons induce air showers that cannot be distinguished from those produced by protons. For this reason, the search for neutrons from a given source is performed by searching for an excess of air showers from the corresponding direction. All these searches have resulted in stringent upper limits on the corresponding fluxes of the considered particles, allowing, together with the results obtained by other experiments, to shed some light on the most energetic phenomena of our Universe. An overview of the Multi-Messenger activities carried out within the Pierre Auger Collaboration is presented.