With the discovery of the Higgs boson at the LHC in 2012, all fundamental parameters of the Standard Model Theory (SMT) have been experimentally measured. Then the global fits of the electroweak sector provide a powerful test of the internal consistency of the SMT. Any observable sensitive to electroweak corrections can be unambiguously predicted and any deviation of the measurements with respect to the predictions would reveal the existence of new, weakly interacting particles. Thus precision electroweak measurements are a key tool for constraining theories describing physics beyond the SMT. Although hadron colliders (Tevatron, LHC) have matched or occasionally exceeded the precision of LEP measurements, e+e- colliders are unrivalled for electroweak precision measurements. The expected performance of the future e+e- collider, FCC-ee, is discussed in the perspective of indirect discovery of new physics. This machine is nevertheless well-suited for direct discoveries as well.