Probing high-energy interactions of atmospheric and astrophysical neutrinos

Astrophysical and atmospheric neutrinos are important probes of the powerful accelerators that produce cosmic-rays with EeV energies. Understanding these accelerators is a key goal of neutrino observatories, along with searches for neutrinos from supernovae, from dark matter annihilation, and other astrophysics topics. Here, we discuss how neutrino observatories like IceCube and future facilities like KM3NeT and IceCube-Gen2 can study the properties of high-energy (above 1 TeV) neutrino interactions. This is far higher than is accessible at man-made accelerators, where the highest energy neutrino beam reached only 500 GeV. In contrast, neutrino observatories have observed events with energies above 5 PeV - 10,000 times higher in energy - and future large observatories may probe neutrinos with energies up to $10^{20}$ eV. These data have implications for both Standard Model measurements, such as of low Bjorken$-x$ parton distributions and gluon shadowing, and also for searches for beyond Standard Model physics. This chapter will review the existing techniques and results, and discuss future prospects.