  High energy photons from astrophysical sources are unique probes for some
predictions of candidate theories of Quantum Gravty (QG). In particular,
imaging atmospheric Cherenkov telescopes (IACTs) are instruments optimised for
astronomical observations in the energy range spanning from a few tens of GeV
to ~100 TeV, which makes them excellent instruments to search for effects of
QG. In this article, we will review QG effects which can be tested with IACTs,
most notably the Lorentz invariance violation and its consequences. It is often
represented and modelled with photon dispersion relation modified by
introducing energy-dependent terms. We will describe the analysis methods
employed in the different studies, allowing for careful discussion and
comparison of the results obtained with IACTs for more than two decades.
Loosely following historical development of the field, we will observe how the
analysis methods were refined and improved over time, and analyse why some
studies were more sensitive than others. Finally, we will discuss the future of
the field, presenting ideas for improving the analysis sensitivity and
directions in which the research could develop.
