`Constraining physics beyond the Standard Model in effective Higgs interactions' Abstract: The discovery of a Higgs(-like) boson has opened new avenues to search for physics beyond the SM. The precise characterization of interactions of the new boson at the LHC and future colliders plays a key role in this endeavour. One very useful approach is the parameterization of new physics via effective theories, e.g. by augmenting the SM with the leading higher-dimensional operators. I give a pedagogical overview over this framework and summarize some existing analyses, as well as caveats and limitations. I will further talk about the implementation of this effective theory into the FITTINO package which addresses some of these issues, and ongoing work to indirectly constrain anomalous triple gauge couplings from Higgs physics.