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The discovery of a cosmic high-energy neutrino flux has opened a new observational window onto the universe, with neutrinos being a key to understanding the origin of the highest-energy cosmic rays and gamma rays. Recent achievements include the identification of two distinctive potential neutrino emitters as well as the first observation of the Milky Way with messengers other than photons. Investigations of cosmic neutrinos can also test fundamental physics, e.g. probing neutrino-nucleon intractions or neutrino oscillations as well as BSM physics, at energies inaccessible with man-made accelerators. In this colloquium, we survey the current status of high-energy neutrino astrophysics, highlighting observational methods and a few recent results. We then outline questions these results have raised and a vision of possible future opportunities in both particle and astro-particle physics.