Recent progress in applying lattice QCD to kaon physics

Standard lattice calculations in kaon physics are based on the evaluation of matrix elements of local operators between two single-hadron states or a single-hadron state and the vacuum. Recent progress in lattice QCD has gone beyond these standard observables. I will review the status and prospects of lattice kaon physics with an emphasis on non-leptonic $K\to \pi \pi$ decay and long-distance processes including $K^0$-$\overline{K^0}$ mixing and rare kaon decays.