  Some models for quantum gravity (QG) violate Lorentz invariance and predict
an energy dependence of the speed of light, leading to a dispersion of
high-energy gamma-ray signals that travel over cosmological distances. Limits
on the dispersion from short-duration substructures observed in gamma-rays
emitted by gamma-ray bursts (GRBs) at cosmological distances have provided
interesting bounds on Lorentz invariance violation (LIV). Recent observations
of unprecedentedly fast flares in the very-high energy gamma-ray emission of
the active galactic nuclei (AGNs) Mkn 501 in 2005 and PKS 2155-304 in 2006
resulted in the most constraining limits on LIV from light-travel observations,
approaching the Planck mass scale, at which QG effects are assumed to become
important. I review the current status of LIV searches using GRBs and AGN flare
events, and discuss limitations of light-travel time analyses and prospects for
future instruments in the gamma-ray domain.
