  We summarize the present status of lattice gauge theory computations of the
leptonic decay constants $f_D$ and $f_B$. The various sources of systematic
errors are explained in a manner easily understood by the non--expert. The
results obtained by the different groups are then systematically compared. As a
result, we derive estimates for $f_D$ and $f_B$ in the quenched approximation
through an appropriate combination of the data available from the different
groups. Since we account for a possible lattice spacing dependence, the final
errors are quite large. However, it is now well known how these uncertainties
can be reduced. For the decay constant of heavy--light pseudoscalar mesons with
masses of 1-2~GeV, an interesting comparison of a full QCD result with the
corresponding simulation in the quenched approximation can be done. Effects of
sea quarks of mass $m_s$ are below the statistical accuracy of these
simulations. Related quantities, like $B$--parameters, the spectrum of
beauty--hadrons and the breaking of the QCD string are discussed briefly.
