  We discuss the interpretation of the LHC Higgs data and the test of the Higgs
mechanism. This is done in a more model-independent approach relying on an
effective Lagrangian, as well as in specific models like composite Higgs models
and supersymmetric extensions of the Standard Model. The proper interpretation
of the data requires the inclusion of higher-order corrections both for the
relevant Higgs parameters and the production and decay processes. We review
recent results obtained within the Collaborative Research Centre / Transregio 9
"Computational Particle Physics".
