  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.
