  Rare kaon decays are an important testing ground of the electroweak flavor
theory: They can provide new signals of CP-violating phenomena. The interplay
of long-distance QCD effects in strangeness-changing transitions can be
analyzed with Chiral Perturbation Theory techniques. In particular, two rare
kaon decays are analyzed: The first decay, K_L -> pi0 e+e-, is being searched
for as a signal of direct Delta S = 1 CP violation. We provide a thorough
updating of the analysis of the three components of the decay: 1) Direct CP
violation, 2) CP violation through the mass matrix and 3) CP-conserving
(two-photon) contributions. First the chiral calculation of the K_S -> pi0 e+e-
rate is updated to include recent results on the nonleptonic amplitude. Then we
systematically explore the uncertainties in this method. The CP-conserving
amplitude remains somewhat uncertain, but present indications are such that
there may be a sizable CP-violating asymmetry in the e+, e- energies from the
interference of CP-conserving and CP-violating amplitudes. This may potentially
be useful in determining whether direct CP violation is present. The second
decay, K_L -> pi0 gamma e+e-, which occurs at a higher rate than the
nonradiative process K_L -> pi0 e+e-, can be a background to CP violation
studies using the latter reaction. The leading order chiral loop contribution
to K_L -> pi0 gamma e+e- is completely calculable.
