High energy neutrinos play a crucial role in the emerging field of multi-messenger astrophysics and fundamental physics at the highest energies. Recent observations by IceCube of an astrophysical flux of neutrinos extending up to PeV energy scales, and of the first possible source of high-energy neutrinos, mark the opening of a new frontier. However, further opportunities await at the EeV (10^18) energy scale, including tests of fundamental physics interactions and revealing the sources of the highest energy cosmic rays. Larger instruments and new techniques will be needed to access these ultrahigh-energy neutrinos, and to study flavor physics at these energies. I will discuss recent results and progress towards building the next generation of neutrino telescopes using radio detection methods.