  The status of lattice calculations for heavy quark systems is reviewed,
focussing on weak matrix elements for leptonic and semi-leptonic decays of
heavy mesons. After an assessment of the main systematic errors, results for
the decay constants $f_D$ and $f_B$, the $B$ parameter describing $B - \bar{B}$
mixing, the Isgur-Wise function and the spectroscopy of heavy baryons are
discussed.
