  Lorentz violation (LV) is predicted by some quantum gravity (QG) candidates,
wherein the canonical energy-momentum dispersion relation, $E^2=p^2+m^2$, is
modified. Consequently, new phenomenons beyond the standard model are
predicted. Especially, the presence of LV highly affects the propagation of
astrophysical photons with very high energies from distant galaxies. In this
paper, we review the updating theoretical and experimental results on this
topic. We classify the effects into three categories: (i) time lags between
photons with different energies; (ii) a cutoff of photon flux above the
threshold energy of photon decay, $\gamma \rightarrow e^++e^-$; (iii) new
patterns in the spectra of multi-TeV photons and EeV photons, due to the
absorption of background lights. As we can see, the details of LV effects on
astrophysical photons depend heavily on the "phase space" of LV parameters.
From observational aspects, nowadays available and upcoming instruments can
study these phenomenons hopefully, and shed light onto LV issues and QG
theories. The most recent progresses and constraints on the ultra-high energy
cosmic rays (UHECRs) are also fully discussed.
