  The coupling of the electromagnetic field to gravity is discussed. In the
premetric axiomatic approach based on the experimentally well established
conservation laws of electric charge and magnetic flux, the Maxwell equations
are the same irrespective of the presence or absence of gravity. In this sense,
one can say that the charge "substratum" and the flux "substratum" are not
influenced by the gravitational field directly. However, the interrelation
between these fundamental substrata, formalized as the {\it spacetime relation}
H=H(F) between the 2-forms of the electromagnetic excitation H and the
electromagnetic field strength F, is affected by gravity. Thus the validity of
the equivalence principle for electromagnetism depends on the form of the
spacetime relation. We discuss the nonlocal and local linear constitutive
relations and demonstrate that the spacetime metric can be accompanied also by
skewon, dilaton, and axion fields. All these premetric companions of the metric
may eventually lead to a violation of the equivalence principle.
