Ongoing LHC searches for the standard model Higgs Boson in WW or ZZ decay 
modes strongly constrain the top-Higgs state predicted in many models with 
new dynamics that preferentially affects top quarks. Such a state couples 
strongly to top-quarks, and is therefore produced through gluon fusion at 
a rate that can be greatly enhanced relative to the rate for the standard 
model Higgs boson. As we discuss in this talk, a top-Higgs state with mass 
less than 300 GeV is excluded at 95% CL if the associated top-pion has a 
mass of 150 GeV, and the constraint is even stronger if the mass of the 
top-pion state exceeds the top-quark mass or if the top-pion decay constant 
is a substantial fraction of the weak scale. Bounds from searches for a 
Higgs boson decaying to photon pairs or from the rare process b -> s photon 
are also very informative.  When combined, these results have significant 
implications for theories with strong top dynamics, such as topcolor-assisted 
technicolor, top-seesaw models, and certain Higgsless models.