  The existence of astrophysical neutrinos with energies of tens of TeV and
higher has been reliably established by the IceCube experiment; the first
confirmations of this discovery are being obtained with the ANTARES and
Baikal-GVD facilities. The observational results do not fully agree with what
was expected before the start of these experiments. The origin of these
neutrinos has not been conclusively established, and simple theoretical models,
popular for decades, cannot explain all observational data. This review
summarizes the experimental results with emphasis on those important for
constraining theoretical models, discusses various scenarios for the origin of
high-energy neutrinos and briefly lists particualr classes of their potential
astrophysical sources. It is demonstrated that the observational data may be
explained if the flux of astrophysical neutrinos includes the contribution of
extragalactic sources, dominating at the highest energies, and the Galactic
component, significant only at neutrino energies <~100 TeV. Other possible
scenarios are also discussed.
