Progress in multi-messenger observations and emission models of blazars

The recent hint of correlated gamma-ray and neutrino emission from the blazar TXS 0506+056 has renewed interest in blazars as the source of high-energy neutrinos, in which the possible neutrino emission involved hadronic acceleration in the jet of blazars. In this review, we summarize the recent advances in the multi-wavelength and neutrino observations of blazars. We focus on the discussion of the current understanding of blazar emission processes in the leptonic and hadronic model. The future multi-messenger observations combining electromagnetic and neutrino measurements will help us to constrain blazar emission models and understand the origins of the high-energy gamma-rays and neutrinos.