After the exciting new discovery of a Higgs-like particle by ATLAS and CMS in 2012, the next step will be to understand its properties by measuring its couplings to the Standard Model particles. Such measurements are still imprecise, but it is worthwhile to contemplate the theoretical ramifications if the values disagree with the Standard Model Higgs. I will illustrate the impact that such couplings could have, with example consequences such as constraints on supersymmetric explanations (and the nonminimal extensions to avoid them) and evidence for an extended electroweak symmetry breaking sector.