This report presents a brief review on the experimental measurements of the
muon neutrino velocities from the OPERA, Fermilab and MINOS experiments and
that of the (anti)-electron neutrino velocities from the supernova SN1987A, and
consequently on the theoretical attempts to attribute the data as signals for
superluminality of neutrinos. Different scenarios on how to understand and
treat the background fields in the effective field theory frameworks are
pointed out. Challenges on interpreting the OPERA result as a signal of
neutrino superluminality are briefly reviewed and discussed. It is also pointed
out that a covariant picture of Lorentz violation may avoid the refutation on
the OPERA experiment.Comment: 10 latex pages. Final version for journal publicatio
