  Lattice quantum chromodynamics provides first principles calculations for
hadrons containing heavy quarks -- charm and bottom quarks. Their mass spectra,
decay rates, and some hadronic matrix elements can be calculated on the lattice
in a model independent manner. In this review, we introduce the effective
theories that treat heavy quarks on the lattice. We summarize results on the
heavy quarkonium spectrum, which verify the validity of the effective theory
approach. We then discuss applications to $B$ physics, which is the main target
of the lattice theory of heavy quarks. We review progress in lattice
calculations of the $B$ meson decay constant, the $B$ parameter, semi-leptonic
decay form factors, and other important quantities.)
