  This article reviews many of the observational constraints on Lorentz
symmetry violation (LV). We first describe the GZK cutoff and other phenomena
that are sensitive to LV. After a brief historical sketch of research on LV, we
discuss the effective field theory description of LV and related questions of
principle, technical results, and observational constraints. We focus on
constraints from high energy astrophysics on mass dimension five operators that
contribute to LV electron and photon dispersion relations at order E/M_Planck.
We also briefly discuss constraints on renormalizable operators, and review the
current and future contraints on LV at order (E/M_Planck)^2.
