Instrumenting a cubic kilometre of ice at the South Pole, the IceCube neutrino observatory has confirmed the existence of a diffuse flux of astrophysical neutrinos at TeV-PeV energies, opening a new window to the cosmos. This flux, along with that of neutrinos produced in interactions of cosmic rays in the upper atmosphere, enable the study of neutrino interactions at energies far beyond that which is achievable with beams produced on Earth. The Glashow resonance, an on-shell production of the W$^{-}$ boson due to the interaction of a $\bar{\nu}_e$ of $\sim$ 6.3 PeV with an electron has been confirmed at $\sim$100:1 odds, while the cross section with which neutrinos interact with nucleons at TeV-PeV energies, as well as the distribution of inelasticity in these interactions have been found to be compatible with Standard Model expectations. The observed zenith dependent deficit in the number of ${\nu}_{\mu}$ ( and $\bar{\nu}_{\mu}$) interacting and contained within the detector at GeV energies has provided measurements of the neutrino oscillation parameters $|\Delta m^2_{32}|$ and sin$^2(\theta_{23})$ at precisions comparable to that of terrestrial accelerator based neutrino beam experiments. The flavour ratio of the astrophysical neutrino flux provides the most stringent probe so far for quantum-gravity-motivated physics. The next great leap in the study of fundamental physics with cosmic neutrinos requires the construction of IceCube-Gen2, ten times larger and extending the sensitivity to EeV energies.