  Photon splitting due to vacuum polarization in the electric field of an atom
is considered. We survey different theoretical approaches to the description of
this nonlinear QED process and several attempts of its experimental
observation. We present the results of the lowest-order perturbation theory as
well as those obtained within the quasiclassical approximation being exact in
the external field strength. The experiment where photon splitting was really
observed for the first time is discussed in details. The results of this
experiment are compared with recent theoretical estimations.
