Precision physics in theory and experiments has provided an indirect access to the Higgs boson of the Standard Model. After the discovery of a Higgs-like state, new perspectives are open for further tests of the Standard Model and in the search for signals from new physics. In the talk, the interplay of electroweak precision observables and measurements of Higgs boson properties is displayed for the Standard Model and supersymmetric extensions. Recent progress in improving the theoretical predictions is reviewed and the impact for coming collider experiments is illustrated in terms of the MSSM.