High-Energy Neutrinos from Blazar Flares and Implications of TXS 0506+056

Motivated by the observation of a $>290$ TeV muon neutrino by IceCube, coincident with a $sim$6 month-long $gamma$-ray flare of the blazar TXS 0506+056, and an archival search which revealed $13 pm 5$ further, lower-energy neutrinos in the direction of the source in 2014-2015, we discuss the likely contribution of blazars to the diffuse high-energy neutrino intensity, the implications for neutrino emission from TXS 0506+056 based on multi-wavelength observations of the source, and a multi-zone model that allows for sufficient neutrino emission so as to reconcile the multi-wavelength cascade constraints with the neutrino emission seen by IceCube in the direction of TXS 0506+056.