  The possibility that there is some Cosmic Polarization Rotation (CPR), i.e.
that the polarization angle rotates while a photon travels in vacuum over large
distances, is important for at least two reasons: first, the polarization angle
seems to be the most steady characteristic of photons and, second, CPR would be
associated with violations of fundamental physical principles, like the
Einstein Equivalence Principle on which all metric theories of gravity are
based, including General Relativity, for which we celebrate the Centennial this
year 2015. We review here the astrophysical tests which have been carried out
to check if CPR exists. These are using the radio and ultraviolet polarization
of radio galaxies and the polarization of the cosmic microwave background (both
E-mode and B-mode). These tests so far have been negative, leading to upper
limits of a couple of degrees on any CPR angle, thereby increasing our
confidence in those physical principles and in the resulting theories,
including General Relativity. We discuss future prospects in detecting CPR or
improving the constraints on it.
