  We present a comprehensive description of the Higgs-boson couplings to
Standard Model fermions and bosons in Randall-Sundrum (RS) models with a Higgs
sector localized on or near the infra-red brane. The analytic results for all
relevant Higgs couplings including the loop-induced couplings to gluons and
photons are summarized for both the minimal and the custodial RS model. The RS
predictions for all relevant Higgs decays are compared with current LHC data,
which already exclude significant portions of the parameter space. We show that
the latest measurements are sensitive to KK gluon masses up to $20\, \rm{TeV}
\times (y_*/3)$ at $95\%$ confidence level for anarchic 5D Yukawa couplings
bounded from above by $|(Y_f)_{ij}| < y_*$. We also derive the sensitivity
levels attainable in the high-luminosity run of the LHC and at a future linear
collider.
