Astrophysical Bounds on Planck Suppressed Lorentz Violations

It is generally believed that Lorentz invariance is an exact symmetry of Nature. Together with the equivalence principle, local Lorentz invariance is one of the assumptions underpinning General Relativity. Several predictions from quantum gravity models have put in question the validity of Lorentz invariance at scales near the Planckian one. A major realization of recent years is that such violations/modifications of Lorentz invariance at high energies are not untestable. On the contrary we now have a wealth of observations (especially in high energy astrophysics) and lab experiments which are able to severely constrain some forms of Lorentz violations. In this talk I shall review the general status of this subject (often called quantum gravity phenomenology), focussing on the most recent constraints from astrophysical observations (using GRB, AGN, SNR and UHECR). Finally I will discuss what we might learn from future observation in high energy astrophysics.