  We review the main theoretical motivations and observational constraints on
Planck scale suppressed violations of Lorentz invariance. After introducing the
problems related to the phenomenological study of quantum gravitational
effects, we discuss the main theoretical frameworks within which possible
departures from Lorentz invariance can be described. In particular, we focus on
the framework of Effective Field Theory, describing several possible ways of
including Lorentz violation therein and discussing their theoretical viability.
We review the main low energy effects that are expected in this framework. We
discuss the current observational constraints on such a framework, focusing on
those achievable through high-energy astrophysics observations. In this context
we present a summary of the most recent and strongest constraints on QED with
Lorentz violating non-renormalizable operators. Finally, we discuss the present
status of the field and its future perspectives.
