Abstract: Neutrinos are unique cosmic messengers that allow to explore the most extreme environments of our Universe. In the past decade, neutrino astronomy has reached a milestone with the discovery of high-energy (TeV-PeV) cosmic neutrinos by the IceCube observatory at the South Pole. The origin of these neutrinos is unknown and subject to much speculation in astroparticle physics. Only recently, IceCube was able to find first compelling evidence of a high-energy neutrino source: the gamma-ray blazar TXS 0506+056. The sum of these observations has implications on the strength and abundance of neutrino sources and their visibility in terms of other messengers: cosmic rays, photons and gravitational waves. Multi-messenger astronomy will play a strong role for future discoveries. In my talk, I will summarize the status of neutrino astronomy and highlight the open questions that can be addressed with next-generation neutrino observatories and detector upgrades. I will emphasize the unique potential of neutrino astronomy as a probe of astrophysics and fundamental physics.