Electroweak precision measurements can be used to probe all sectors of Standard Model through quantum correction, as well as put constraints on a wide range of new physics models. This presentation will give an overview of the current state of such electroweak fits and of the theoretical calulations needed to interpret the experimental inputs. Furthermore, proposals for future lepton colliders (FCC-ee, CEPC, ILC) aim for significantly improved precision for measurements of Z-, W- and Higgs boson properties. The statistical power of these measurements would probe physics beyond the Standard Model at multi-TeV scales, in many cases well beyond the reach of the LHC. I will try to delineate the required improvements and innovations on the theory side for the FCC-ee/CEPC/ILC physics program.