  As a basic symmetry of Einstein's theory of special relativity, Lorentz
invariance has withstood very strict tests. But there are still motivations for
such tests. Firstly, many theories of quantum gravity suggest violations of
Lorentz invariance at the Planck energy scale. Secondly, even minute deviations
from Lorentz symmetry can accumulate as particle travel across large distances,
leading to detectable effects at attainable energies. Thanks to their long
baselines and high-energy emission, astrophysical observations provide
sensitive tests of Lorentz invariance in the photon sector. In this paper, I
briefly introduce astrophysical methods that we adopted to search for
Lorentz-violating signatures, including vacuum dispersion and vacuum
birefringence.
