Since the previous kaon conference in 2009, there has been very significant improvement in the precision which can be reached in lattice simulations for standard physical quantities, such as quark masses, the leptonic decay constants, B K and the form factors for K 3 decays. In this talk I focus on quantities which have not been previously computed in lattice computations and for which the RBC-UKQCD collaborations are developing the necessary theoretical and computational framework. There are rare-kaon decays and the long-distance contributions to the K L -K S mass splitting, ∆m K . For ∆m K exploratory numerical studies have been performed to test the techniques and to gain some understanding of the precision which might be reached. For rare kaon decay amplitudes the exploratory work is now beginning.