  The exploration of the universe has recently entered a new era thanks to the
multi-messenger paradigm, characterized by a continuous increase in the
quantity and quality of experimental data that is obtained by the detection of
the various cosmic messengers (photons, neutrinos, cosmic rays and
gravitational waves) from numerous origins. They give us information about
their sources in the universe and the properties of the intergalactic medium.
Moreover, multi-messenger astronomy opens up the possibility to search for
phenomenological signatures of quantum gravity. On the one hand, the most
energetic events allow us to test our physical theories at energy regimes which
are not directly accessible in accelerators; on the other hand, tiny effects in
the propagation of very high energy particles could be amplified by
cosmological distances. After decades of merely theoretical investigations, the
possibility of obtaining phenomenological indications of Planck-scale effects
is a revolutionary step in the quest for a quantum theory of gravity, but it
requires cooperation between different communities of physicists (both
theoretical and experimental). This review is aimed at promoting this
cooperation by giving a state-of-the art account of the interdisciplinary
expertise that is needed in the effective search of quantum gravity footprints
in the production, propagation and detection of cosmic messengers.
