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The astrophysical neutrinos discovered by IceCube have the highest detectedneutrino energies --- from TeV to PeV --- and likely travel the longestdistances --- up to a few Gpc, the size of the observable Universe. Thesefeatures make them naturally attractive probes of fundamental particle-physicsproperties, possibly tiny in size, at energy scales unreachable by any othermeans. The decades before the IceCube discovery saw many proposals ofparticle-physics studies in this direction. Today, those proposals have becomea reality, in spite of astrophysical unknowns. We will showcase examples ofdoing fundamental neutrino physics at these scales, including some of the moststringent tests of physics beyond the Standard Model. In the future, largerneutrino energies --- up to tens of EeV --- could be observed with largerdetectors and further our reach.

Fundamental physics with high-energy cosmic neutrinos today and in the future