We demonstrate a number of effective field theory constructions developed to
capture the effects of new physics on the Higgs sector of the standard
model. We demonstrate that as the self couplings of the Higgs
could be significantly effected by new physics, novel phenomenology such as
a two Higgs bound state (Higgsium) may be possible.
We also demonstrate that the effects of new physics
on the Higgs fermion couplings, and thus the Higgs width, could be significant.
We show that it is possible this could happen while the new physics
cannot be directly detected at LHC. This could lead to an early Higgs discovery
or a missing Higgs in the first 100 fb^(-1) of data at LHC.