  High-energy astrophysics observations provide the best possibilities to
detect a very small violation of Lorentz invariance, such as may be related to
the structure of space-time near the Planck scale. I discuss the possible
signatures of Lorentz invariance violation that can be manifested by observing
the spectra, polarization, and timing of gamma-rays from active galactic nuclei
and gamma-ray bursts. Other sensitive tests are provided by observations of the
spectra of ultrahigh-energy cosmic rays and very high-energy neutrinos. I also
discuss a new time-of-flight analysis of observations of GRB 090510 by the
Fermi gamma-ray Space Telescope. These results, based on high-energy
astrophysical observations, have fundamental implications for space-time
physics and quantum gravity models.
