High-Energy Astrophysical Tests of Lorentz Symmetry

igh-energy cosmic messengers, such as gamma rays, neutrinos, and cosmic rays, have become indispensable tools for probing fundamental physics, providing a natural laboratory that far exceeds the reach of terrestrial particle accelerators. Owing to their extreme energies and vast propagation baselines, which can amplify tiny Planck-scale effects, these messengers offer some of the most promising avenues for testing theories of quantum gravity and for exploring the nature of spacetime itself. In this review, I present a critical synthesis of current constraints on deviations from Lorentz invariance, with emphasis on propagation-based observables such as modified interaction thresholds and time-of-flight effects. Particular attention is devoted to astrophysical uncertainties that may affect the interpretation of these observations, and to what these constraints reveal about the viability of detecting quantum-gravity--induced modifications to spacetime symmetries.