  We review the methods used to test for the existence of cosmological
birefringence, i.e. a rotation of the plane of linear polarization for
electromagnetic radiation traveling over cosmological distances, which might
arise in a number of important contexts involving the violation of fundamental
physical principles. The main methods use: (1) the radio polarization of radio
galaxies and quasars, (2) the ultraviolet polarization of radio galaxies, and
(3) the cosmic microwave background polarization. We discuss the main results
obtained so far, the advantages and disadvantages of each method, and future
prospects.
