I review recent results from experiments on rare decays of kaons,
concentrating on searches for lepton flavor violation (LFV) and on measurements
of quark mixing (CKM) matrix elements. The LFV results are the culmination of
15 years of experimentation at Brookhaven National Laboratory and are unlikely
to be improved upon soon. The CKM studies derive from measurements of decay
rates of charged and neutral kaons into lepton anti-lepton pairs, both with and
without a charged or neutral pion. I discuss recent results and prospects for
improved measurements that could provide an unambiguous test of the Standard
Model explanation for CP violation. This paper is the written version of a talk
presented at the Lepton-Photon Conference in August 1999.Comment: Written version of a talk at the 1999 Lepton Photon Conferenc