  High-energy astrophysical neutrinos have been observed by several telescopes
in the last decade, but their sources still remained unknown. We address the
problem of locating astrophysical neutrinos' sources in a statistical manner.
We show that blazars positionally associated with IceCube neutrino detections
have stronger parsec-scale radio cores than the rest of the sample. The
probability of a chance coincidence is only 4*10^-5 corresponding to a
significance of 4.1 sigma. We explicitly list four strong radio blazars as
highly probable sources of neutrinos above 200 TeV: 3C 279, NRAO 530, PKS
1741-038, and PKS 2145+067. There are at least 70 more radio-bright blazars
that emit neutrinos of lower energies, starting from TeVs. Using continuous
RATAN-600 monitoring of VLBI-selected blazars, we find that radio flares at
frequencies above 10 GHz coincide with neutrino arrival dates. The most
pronounced example of such behavior is PKS 1502+106 that experienced a major
flare in 2019. We demonstrate that the majority of IceCube astrophysical
neutrino flux derived from muon-track analyses may be explained by blazars,
that is, AGNs with bright Doppler-boosted jets. High-energy neutrinos can be
produced in photohadronic interactions within parsec-scale relativistic jets.
Radio-bright blazars associated with neutrino detections have very diverse
gamma-ray properties, which suggests that gamma-rays and neutrinos may be
produced in different regions of blazars and not directly related. A narrow jet
viewing angle is, however, required to detect either of them. We conclude with
discussion of recent independent tests and extensions of our findings.

High Energy Astrophysical Phenomena;Astrophysics of Galaxies