  We review and discuss recent results on the search for correlations between
astrophysical neutrinos and gamma-ray-detected sources, with many
extra-galactic studies reporting potential associations with different types of
blazars. We investigate possible dependencies on blazar sub-classes by using
the largest catalogues and all the multi-frequency data available. Through the
study of similarities and differences in these sources we conclude that blazars
come in two distinct flavors: LBLs and IHBLs (low-energy-peaked and
intermediate-high-energy-peaked objects). These are distinguished by widely
different properties such as the overall spectral energy distribution shape,
jet speed, cosmological evolution, broad-band spectral variability, and optical
polarization properties. Although blazars of all types have been proposed as
neutrino sources, evidence is accumulating in favor of IHBLs being the
counterparts of astrophysical neutrinos. If this is indeed the case, we argue
that the peculiar observational properties of IHBLs may be indirectly related
to proton acceleration to very high energies.
