  I report on the application of tmQCD techniques to the computation of
hadronic matrix elements of four-fermion operators. Emphasis is put on the
computation of $B_K$ in quenched QCD performed by the ALPHA Collaboration. The
extension of tmQCD strategies to the study of neutral $B$-meson mixing is
briefly discussed. Finally, some remarks are made concerning proposals to apply
tmQCD to the computation of $K\to\pi\pi$ amplitudes.
