Heavy Quark Physics on the Lattice

I review the current status of lattice calculations of the properties of bound states containing one or more heavy quarks. Many of my remarks focus on the heavy-light leptonic decay constants, such as $f_B$, for which the systematic errors have by now been quite well studied. I also discuss $B$-parameters, semileptonic form factors, and the heavy-light and heavy-heavy spectra. Some of my ``world averages'' are: $f_B=200(30) MeV$, $f_B\sqrt{\hat B_{B_d}}= 230(40) MeV$, $f_{B_s}/f_B=1.16(4)$ and $f_{B_s}\sqrt{\hat B_{B_s}}/f_B\sqrt{\hat B_{B_d}}=1.16(5)$.