  The propagation of $\gamma$ rays over very large distances provides new
insights on the intergalactic medium and on fundamental physics. On their path
to the Earth, $\gamma$ rays can annihilate with diffuse infrared or optical
photons of the intergalactic medium, producing $e^+ \, e^-$ pairs. The density
of these photons is poorly determined by direct measurements due to significant
galactic foregrounds. Studying the absorption of $\gamma$ rays from
extragalactic sources at different distances allows the density of low-energy
diffuse photons to be measured. Gamma-ray propagation may also be affected by
new phenomena predicted by extensions of the Standard Model of particle
physics. Lorentz Invariance is violated in some models of Quantum Gravity,
leading to an energy-dependent speed of light in vacuum. From differential
time-of-flight measurements of the most distant $\gamma$-ray bursts and of
flaring active galactic nuclei, lower bounds have been set on the energy scale
of Quantum Gravity. Another effect that may alter $\gamma$-ray propagation is
predicted by some models of String Theory, namely the mixing of the $\gamma$
ray with a light fundamental boson called an "axion-like particle", which does
not interact with low-energy photons. Such a mixing would make the Universe
more transparent to $\gamma$ rays than what would otherwise be, in a sense it
decreases the amount of modification to the spectrum that comes from the
extragalactic background light. The present status of the search for all these
phenomena in $\gamma$-ray astronomy is reviewed.
