Precision calculations for Higgs physics in the standard model and beyond

At least since the discovery of the Higgs boson at the Large Hadron Collider at CERN, the Higgs sector of the Standard Model of particle physics has become one of the central research areas of high energy physics. Deviations between measurement and theoretical prediction within this sector have the potential to become a window on the quantum field theories describing nature. Besides the increasing precision of measurements, high-precision predictions are required to become sensitive on possible deviations. The focus of this work is on precise predictions of observables within the Higgs sector. On the one hand, studies of Higgs mass calculations within the context of the minimal supersymmetric extension of the Standard Model are presented, which include partial three-loop contributions. Different kinds of calculational methods are introduced, which, when combined, yield a reliable prediction of the light CP-even Higgs mass for in principle arbitrary parameter configurations. Utilizing the results of this work, the relative uncertainty of the predicted mass of the light CP-even Higgs can be reduced below the 1% level. Additionally, all corresponding results are implemented in an open-source program, which allows for further studies. Moreover, Higgs production in association with a vector boson at the Large Hadron Collider at CERN is studied. By exploiting a symmetry connecting the final state gauge bosons, a particular observable can be defined, that leads to the cancellation of various sources of uncertainty in both measurement and prediction. For illustration, an experimental analysis for this observable is performed, which demonstrates an increased sensitivity to possible deviations between measurement and prediction, and, in addition, yields to evidence for the production of a Higgs boson associated with a Z boson through gluon fusion. Finally, the recent progress in the calculation of two-loop corrections to Higgs-Z production via gluon fusion including the full top-quark mass dependence are presented. To include these quark-mass effects, novel algebraic methods are developed and provided with an implementation into an open-source program, that can find wide application in the calculation of multi-loop Feynman diagrams.