Tests of Lorentz invariance: a 2013 update

We present an updated review of Lorentz invariance tests in effective field theories (EFTs) in the matter as well as in the gravity sector. After a general discussion of the role of Lorentz invariance and a derivation of its transformations along the so-called von Ignatovski theorem, we present the dynamical frameworks developed within local EFT and the available constraints on the parameters governing the Lorentz breaking effects. In the end, we discuss two specific examples: the OPERA 'affaire' and the case of Hořava- Lifshitz gravity. The first case will serve as an example, and a caveat, of the practical application of the general techniques developed for constraining Lorentz invariance violation to a direct observation potentially showing these effects. The second case will show how the application of the same techniques to a specific quantum gravity scenario has far-reaching implications not foreseeable in a purely phenomenological EFT approach