  Standard lattice calculations in flavour physics or in studies of hadronic
structure are based on the evaluation of matrix elements of local composite
operators between hadronic states or the vacuum. In this talk I discuss
developments aimed at the computation of long-distance, and hence non-local,
contributions to such processes. In particular, I consider the calculation of
the $K_L$-$K_S$ mass difference $\Delta m_K=m_{K_L}-m_{K_S}$ and the amplitude
for the rare-kaon decay processes $K\to\pi\ell^+\ell^-$, where the lepton
$\ell=e$ or $\mu$. Lattice calculations of the long-distance contributions to
the indirect $CP$-violating parameter $\epsilon_K$ and to the rare decays
$K\to\pi\nu\bar\nu$ are also beginning. Finally I discuss the possibility of
including $O(\alpha)$ electromagnetic effects in computations of leptonic and
semileptonic decay widths, where the novel feature is the presence of infrared
divergences. This implies that contributions to the width from processes with a
real photon in the final state must be combined with those with a virtual
photon in the amplitude so that the infrared divergences cancel by the
Bloch-Nordsieck mechanism. I present a proposed procedure for lattice
computations of the $O(\alpha)$ contributions with control of the cancellation
of the infrared divergences.
