Active galactic nuclei (AGN) with relativistic jets are the most powerful persistent astrophysical sources of electromagnetic radiation in the Universe. Blazars are the most extreme subclass of AGN with jets directed along the line of sight of the observer. Their high-energy photon emission dominates the extragalactic gamma-ray sky and reaches multi-TeV energies. This demonstrates that blazars accelerate particles to very high energies. It has long been suspected that blazars may also accelerate protons to very high energies and thus be cosmic neutrino sources. Being extremely rare objects in addition to being bright, blazars are among the most readily testable neutrino candidate source classes. Several multi-messenger monitoring campaigns have recently been triggered in response to high-energy neutrinos observed with the IceCube Neutrino Observatory from the direction of blazars. In this contribution, I summarise the theoretical interpretation of these observations and give an overview of the possible role of blazars as neutrino sources in light of the experimental results.