  Commensurate scale relations are perturbative QCD predictions which relate
observable to observable at fixed relative scale, such as the "generalized
Crewther relation", which connects the Bjorken and Gross-Llewellyn Smith deep
inelastic scattering sum rules to measurements of the e+ e- annihilation cross
section. We show how conformal symmetry provides a template for such QCD
predictions, providing relations between observables which are present even in
theories which are not scale invariant. All non-conformal effects are absorbed
by fixing the ratio of the respective momentum transfer and energy scales. In
the case of fixed-point theories, commensurate scale relations relate both the
ratio of couplings and the ratio of scales as the fixed point is approached. In
the case of the $\alpha_V$ scheme defined from heavy quark interactions,
virtual corrections due to fermion pairs are analytically incorporated into the
Gell-Mann Low function, thus avoiding the problem of explicitly computing and
resumming quark mass corrections related to the running of the coupling.
Applications to the decay width of the Z boson, the BFKL pomeron, and virtual
photon scattering are discussed.
