This contribution reviews recent advances in the possible identification of blazars as potential sources of at least some of the very-high-energy neutrinos detected by the IceCube neutrino detector at the South Pole. The basic physical requirements for neutrino production and physics constraints that may be drawn from neutrino -blazar associations are reviewed. Several individual cases of possible associations will be discussed in more detail. It is emphasized that due to γγ opacity constraints in efficiently neutrinoproducing blazars, an association between X-ray -soft γ-ray activity and very-high-energy neutrino production is more naturally expected than a connection between neutrino and high-energy/very-high-energy γ-ray activity.