  Many new physics models predict sizable modifications to the SM Zbb
couplings, while the corresponding measurements at LEP and SLC exhibit some
discrepancy with the SM predictions. After updating the current results on the
Zbb coupling constraints from global fits, we list the observables that are
most important for improving the Zbb coupling constraints and estimate the
expected precision reach of three proposed future e+e- colliders, CEPC, ILC and
FCC-ee. We consider both the case that the results are SM-like and the one that
the Zbb couplings deviate significantly from the SM predictions. We show that,
if we assume the value of the Zbb couplings to be within 68% CL of the current
measurements, any one of the three colliders will be able to rule out the SM
with more than 99.9999% CL (5 sigma). We study the implications of the improved
Zbb coupling constraints on new physics models, and point out their
complementarity with the constraints from the direct search of new physics
particles at the LHC, as well as with Higgs precision measurements. Our results
provide a further motivation for the construction of future e+e- colliders.
