Abstract: I will present an analysis of the 2011 LHC Higgs data in the context of an effective low-energy theory of the Higgs boson. The focus will be on the 4-leptons and diphoton channels at the LHC and the b-bar channel at the Tevatron. Combining the available data in these channels, one can derive constraints on the effective theory parameters. These constraints can then be mapped several simplified scenarios of natural new physics capturing the Higgs physics of simple supersymmetric and composite Higgs models. I will also discuss the phenomenological consequences of the assumption that the Higgs couplings to the electroweak gauge bosons is larger than in the Standard Model. The latter may be hinted at by the CMS diphoton channel excess in the dijet category, and by the Tevatron excess in the W/Z+H -> b-bar channel.