Active galactic nuclei (AGN) are one of the most promising classes of extragalactic cosmic-ray accelerators. This has been recently strengthened by increasing indications that AGN, and in particular blazars, may be sources of IceCube neutrinos. In this talk I report on recent results from self-consistent leptohadronic modeling of a large sample of blazar AGN, where the observed multi-wavelength spectrum is described by means of a self-consistent numerical radiation model of cosmic-ray interactions. First, I discuss recent results from the modeling of a sample of 324 gamma-ray-bright blazars, of which 237 are flat-spectrum radio quasars (FSRQs). By fitting multi-wavelength observations from optical to gamma rays compiled in a previous work, we can constrain the source parameters, estimate the possible contribution from cosmic-ray protons, and predict the corresponding neutrino emission. For about one-third of the blazars in the sample, cascades from hadronic interactions can help explain observations in the X-ray band, in agreement with recent results on individual IceCube candidates. For the rest of the sources, the observed spectra are well described by purely leptonic emission. By extrapolating from these results, we can also predict the diffuse neutrino flux from the entire blazar population, which is at the level of 20\% of the diffuse flux observed by IceCube. I discuss the general implications of these results for the next generation of neutrino experiments, like IceCube-Gen2.