  Possible violations of fundamental physical principles, e.g. the Einstein
equivalence prin- ciple on which all metric theories of gravity are based,
including general relativity (GR), would lead to a rotation of the plane of
polarization for linearly polarized radiation traveling over cosmological
distances, the so-called cosmic polarization rotation (CPR). We review here the
astrophysical tests which have been carried out so far 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 the order of
one degree on any CPR angle, thereby increasing our confidence in those
physical principles, including GR. We also discuss future prospects in
detecting CPR or improving the constraints on it.
