Searching for New Physics with Kaons

I will review new developments in lattice simulations in kaon physics designed to explore the limits of the Standard Model and to search for signatures of new physics. For the decays of kaons (and pions) into leptons, the precision of lattice computations is now such that electromagnetic and strong isospin-breaking corrections must be included if further progress is to be made in extracting fundamental physics from experimental measurements. I will also discuss the RBC-UKQCD collaborations' program evaluating the long- distance contributions to a variety of quantities including the K_L-K_S mass difference, the indirect CP-violation parameter epsilon_K and rare kaon decay amplitudes. Finally I will present the status of the same collaborations' computations of kaon decays into two pions, including the first calculation of the direct CP-violating parameter epsilon'/epsilon.