  This talk opens the CosPA2011 session on OPERA's superluminal neutrino claim.
I summarize relevant observations and constraints from OPERA, MINOS, ICARUS,
KamLAND, IceCube and LEP as well as observations of SN1987A. I selectively
review some models of neutrino superluminality which have been proposed since
OPERA's announcement, focusing on a neutrino dark energy model. Powerful
theoretical constraints on these models arise from Cohen-Glashow bremsstrahlung
and from phase space requirements for the initial neutrino production. I
discuss these constraints and how they might be evaded in models in which the
maximum velocities of both neutrinos and charged leptons are equal but only
superluminal inside of a dense medium.
