Global Fits of the Electroweak Standard Theory: Past, Present and Future

The last decades have seen tremendous progress in the experimental techniques for measuring key observables of the Standard Theory (ST) as well as in theoretical calculations that has led to highly precise predictions of these observables. Global electroweak fits of the ST compare the precision measurements of electroweak observables from lepton and hadron colliders at CERN and elsewhere with accurate theoretical predictions of the ST calculated at multi-loop level. For a long time, global fits have been used to assess the validity of the ST and to constrain indirectly (by exploiting contributions from quantum loops) the remaining free ST parameters, like the masses of the top quark and Higgs boson before their direct discovery. With the discovery of the Higgs boson at the Large Hadron Collider (LHC), the electroweak sector of the ST is now complete and all fundamental ST parameters are known. Hence the global fits are a powerful tool to probe the internal consistency of the ST, to predict ST parameters with high precision, and to constrain theories describing physics beyond the ST. In this chapter we review the global fits of the electroweak sector of the ST from an experimentalist's perspective. We briefly recall the most important achievements from the past (mainly driven by the precise measurements of Z pole observables), discuss the present situation after the accurate measurements of the top quark and Higgs boson masses, and present prospects of the fits as expected from new measurements at the LHC and future lepton colliders.