We review and discuss recent results on the search for correlations between astrophysical neutrinos and γ-ray-detected sources, with many extragalactic 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 flavours: 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 polarisation properties. Although blazars of all types have been proposed as neutrino sources, evidence is accumulating in favour 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.