There is vast potential in high-energy cosmic neutrinos to test astrophysics and particle physics. The cosmic neutrinos discovered by IceCube have the highest detected neutrino energies---up to a few PeV---and travel the longest distances---up to a few Gpc, the size of the observable Universe. These features make them incisive probes of the conditions inside the most energetic and distant non-thermal astrophysical sources, and of particle-physics properties, possibly tiny in size and at energy scales unreachable by other means. The decades before the IceCube discovery saw many proposals of studies in these directions. Today, these proposals have become a reality, and we are turning them into data-driven tests. I will showcase examples of testing astrophysics and particle physics at these scales, including constraining the physical conditions in the still-unidentified astrophysical neutrino sources and probing physics beyond the Standard Model. Thanks to a rich experimental program, the discovery of neutrinos with energies a thousand times higher in the coming decade could push our reach even further.