I will review the RBC-UKQCD programme of computations of long-distance contributions to physical processes, focussing on the rare kaon decays $K\to\pi\mu^+\mu^-$ and $K\to\pi\nu\bar{\nu}$. The underlying theoretical framework, which includes issues such as the matching of short and long distance contributions, finite-volume corrections and the presence of unphysical terms in the correlation functions which grow with the time range, will be discussed. Results from exploratory simulations will be presented together with a discussion of the collaboration’s plans and prospects for future computations.