Lorentz Invariance Violation (LIV) may be a good observational window on
Quantum Gravity physics. Within last few years, all major Gamma-ray experiments
have published results from the search for LIV with variable astrophysical
sources: gamma-ray bursts with detectors on-board satellites and Active
Galactic Nuclei with ground-based experiments. In this paper, the recent
time-of-flight studies with unpolarized photons published from the space and
ground based observations are reviewed. Various methods used in the time delay
searches are described, and their performance discussed. Since no significant
time-lag value was found within experimental precision of the measurements, the
present results consist of 95% confidence cevel limits on the Quantum Gravity
scale on the linear and quadratic terms in the standard photon dispersion
relations.Comment: 22 pages, 9 figures. V2 match the published version. Invited review
talk to the 2nd International Colloquium "Scientific and Fundamental Aspects
of the Galileo Programme", 14-16 october 2009, Padua, Ital