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Throughout the last century, increasingly powerful particle accelerators revealed fundamental particles, interactions, and symmetries. Still, ample territory remains unexplored at higher energies, ripe for discoveries. Today, accelerators still churn out valuable data, but have yet to significantly further our understanding of fundamental physics. Observing particle processes at higher energies would provide guidance, but they lie beyond the reach of accelerator technology. Fortunately, high-energy (TeV-PeV) and ultra-high-energy (> 100 PeV) neutrinos of cosmic origin have a vast potential to probe fundamental physics in new regimes of energy and distance, otherwise unreachable. Today, we are already tapping into this potential, thanks to recent discoveries by the IceCube neutrino telescope. In the coming decade, we will enter a regime of higher statistics and may extend our reach to ultra-high energies, thanks to an ambitious experimental program currently under planning. By means of illustration, I will survey the rich landscape of high-energy physics with cosmic neutrinos, from the perspectives of theory and experiment. Along the way, I will point out manifest instances of the natural synergy between low-energy and high-energy neutrino experiments, and the importance of accounting for astrophysical unknowns.