  We discuss the experimental and theoretical uncertainties on precision
electroweak observables and their relationship to the indirect constraints on
the Higgs-boson mass, $\MH$, in the Standard Model (SM). The critical
experimental measurements ($\MW$, $\sweff$, $\mt$, ...) are evaluated in terms
of their present uncertainties and their prospects for improved precision at
future colliders, and their contribution to the constraints on $\MH$. In
addition, the current uncertainties of the theoretical predictions for $\MW$
and $\sweff$ due to missing higher order corrections are estimated and
expectations and necessary theoretical improvements for future colliders are
explored. The constraints from rare B decays are also discussed. Analysis of
the present experimental and theoretical precisions yield a current upper bound
on $\MH$ of $\sim 200$ GeV. Including anticipated improvements corresponding to
the prospective situation at future colliders (Tevatron Run II, LHC, LC/GigaZ),
we find a relative precision of about 25% to 8% (or better) is achievable in
the indirect determination of $\MH$.
