Neutrinos of astrophysical origin are messengers produced in stars, in explosive phenomena like core-collapse supernovae, in the accretion disks around black holes, or in the Earth's atmosphere. Their fluxes and spectra encode information on the environments that produce them. Such fluxes are modified in characteristic ways when neutrinos traverse a medium. Here the current understanding of neutrino flavour conversion in media is summarized. The importance of this domain for astrophysical observations is emphasized. Examples are given of the fundamental properties that research into astrophysical neutrinos has uncovered, or might reveal in the future.