  We consider here the possibility of quantum gravity induced violation of
Lorentz symmetry (LV). Even if suppressed by the inverse Planck mass such LV
can be tested by current experiments and astrophysical observations. We review
the effective field theory approach to describing LV, the issue of naturalness,
and many phenomena characteristic of LV. We discuss some of the current
observational bounds on LV, focusing mostly on those from high energy
astrophysics in the QED sector at order E/M_Planck. In this context we present
a number of new results which include the explicit computation of rates of the
most relevant LV processes, the derivation of a new photon decay constraint,
and modification of previous constraints taking proper account of the helicity
dependence of the LV parameters implied by effective field theory.
