Abstract One of the key open questions in fundamental physics concerns the supposed quantum structure of spacetime. New physical effects are expected as residual evidence of a more fundamental theory of nature. In this fundamental theory the underlying physical symmetries could be modified by the quantized structure of geometry. One of the most important symmetries in our description of Physics is Lorentz Invariance (LI). Nowadays LI is at the root of our understanding of nature and underlies its physical description. Even if there is no definitive evidence to sustain departures from this symmetry, there are consistent points indicating that Lorentz Invariance Violation (LIV) can be a consequence of quantum gravity. A critical issue concerns therefore the necessity of testing this fundamental symmetry validity. Ultra High Energy Cosmic Rays (UHECR) and neutrino flavor oscillation are promising physical processes of investigation for LIV, since the high energy involved and the interaction of different particle species.