Constraints on models of the origin of high-energy astrophysical neutrinos

The existence of astrophysical neutrinos with energies of tens of TeV and higher has been firmly established by the IceCube experiment; the first confirmations of this discovery were obtained by the ANTARES and Baikal-GVD installations. At the same time, observational results do not fully agree with those expected before the start of these experiments. The origin of the neutrino has not yet been determined, while simple theoretical models, popular for decades, cannot explain the entire ensemble of observational data. In the present review, a summary of experimental results is given with a particular emphasis on those most relevant for constraining theoretical models; features of various scenarios of the origin of high-energy neutrinos are discussed; and particular classes of their potential astrophysical sources are briefly listed. It is shown that observational data may be explained if the astrophysical neutrino flux includes both a contribution of extragalactic sources, dominant at high energies, and a Galactic component, essential only at neutrino energies $\lesssim 100$ TeV. Other possible scenarios are also discussed.