Review of electroweak fits of the SM and beyond, after the Higgs discovery -- with Gfitter

We present an update of the global Standard Model (SM) fit to electroweak precision data under the assumption that the new particle discovered at the LHC is the SM Higgs boson. In this scenario all parameters entering the calculations of electroweak precision observables are known, allowing to over-constrain the SM at the electroweak scale and to assert its validity. Within the SM the W boson mass and the effective weak mixing angle can now be accurately predicted from the global fit. Their results exceed in precision the direct measurements. A determination of the S , T and U parameters, which parametrize the oblique vacuum corrections, is given. We examine the impact of the STU observables on a model of modified couplings of the Higgs boson to gauge bosons, and compare this with the corresponding analysis of LHC measurements of the signal strength of Higgs channels. Future measurements at the International Linear Collider (ILC) promise to improve significantly the experimental precision of key observables used in the fit. We conclude with an outlook to the global electroweak fit for the ILC with GigaZ option.