  A number of different approaches to quantum gravity are at least partly
phenomenologically characterized by their treatment of Lorentz symmetry, in
particular whether the symmetry is exact or modified/broken at the smallest
scales. For example, string theory generally preserves Lorentz symmetry while
analog gravity and Lifshitz models break it at microscopic scales. In models
with broken Lorentz symmetry there are a vast number of constraints on
departures from Lorentz invariance that can be established with low energy
experiments by employing the techniques of effective field theory in both the
matter and gravitational sectors. We shall review here the low energy effective
field theory approach to Lorentz breaking in these sectors and present various
constraints provided by available observations.
