  I review the theoretical basis of the prediction that the decay K_L -> pi+
pi- e+ e- should show a large CP- and T-violation, a prediction now confirmed
by the KTeV experiment. The genesis of the effect lies in a large violation of
CP- and T-invariance in the decay K_L -> pi+ pi- gamma, which is encrypted in
the polarization state of the photon. The decay K_L -> pi+ pi- e+ e- serves as
an analyser of the photon polarization. The asymmetry in the distribution of
the angle phi between the pi+ pi- and e+ e- planes is a direct measure of the
CP-odd, T-odd component of the photon's Stokes vector. A complete study of the
angular distribution can reveal further CP-violating features, which probe the
non-radiative (charge-radius and short-distance) components of the K_L -> pi+
pi- e+ e- amplitude.
