The discovery of 0.1 – 2 PeV neutrinos of astrophysical origin by IceCube has opened a new window in the high-energy Universe. There are various astrophysical candidate sources, including active galactic nuclei (AGN) and starburst galaxies. Although a firm association of the detected neutrinos with one (or more) of them is still lacking, IceCube has started constraining various theoretical models. In this talk, I will present our model predictions for (i) the blazar contribution to the diffuse neutrino flux and (ii) for the possibility of detecting individual blazars as neutrino point sources. I will discuss the implications of the latest IceCube searches on the theoretical models for blazar emission.