  In this brief, and by no means complete, review I discuss situations in
string theory, in which Lorentz Invariance Violation may occur in a way
consistent with world-sheet conformal invariance, thereby leading to
acceptable, in principle, string backgrounds. In particular, I first discuss
spontaneous Lorentz violation in (non supersymmetric) open string field theory.
Then, I move onto a discussion of gravity-induced modified dispersion relations
in non-critical (Liouville) strings, in the sense of an induced Finsler-like
geometry depending on both coordinates and momenta, for string propagation in
non-trivial space times (such as D-particle ``foamy situations''). I pay
attention to explaining the appearance of bi-metric models from such string
theories, which could serve as examples of alternative scenaria to dark matter.
Finally, I make some comparisons with similar developments in other contexts,
such as critical strings in non-commutative space times, as well as deformed
special relativities and theories with reduced Lorentz symmetry, advocated
recently, where again Finsler geometry seems to come into play. In this latter
respect, I put the emphasis on phenomenology and attempt to answer the question
as to whether there is the possibility of experimental disentanglement of the
various approaches.
