  Lattice QCD should allow a derivation of the $\Delta I=1/2$ rule from first
principles, but numerical calculations to date have been plagued by a variety
of problems. After a brief review of these problems, we present several new
methods for calculating $K\to\pi\pi$ amplitudes. These are designed for Wilson
fermions, though they can be used also with staggered fermions. They all
involve a non-perturbative determination of matching coefficients. We show how
problems of operator mixing can be greatly reduced by using point-split
hadronic currents, and how CP violating parts of the $K\to\pi\pi$ amplitudes
can be calculated by introducing a fake top quark. Many of the methods can also
be applied to the calculation of two body non-leptonic B-meson decays.
