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The topic of Lorentz invariance violation is a fundamental question inphysics that has taken on particular interest in theoretical explorations ofquantum gravity scenarios. I discuss various gamma-ray observations that givelimits on predicted potential effects of Lorentz invariance violation. Amongthese are spectral data from ground based observations of the multi-TeVgamma-rays from nearby AGN, INTEGRAL detections of polarized soft gamma-raysfrom the vicinity of the Crab pulsar, Fermi Gamma Ray Space Telescope studiesof photon propagation timing from gamma-ray bursts, and Auger data on thespectrum of ultrahigh energy cosmic rays. These results can be used toseriously constrain or rule out some models involving Planck scale physics.Possible implications of these limits for quantum gravity and Planck scalephysics will be discussed.

Gamma-ray and Cosmic-ray Tests of Lorentz Invariance Violation and Quantum Gravity Models and Their Implications