  We examine trilinear and quartic anomalous gauge couplings (AGCs) generated
in composite Higgs models and models with warped extra dimensions. We first
revisit the SU(2)_L x U(1)_Y effective Lagrangian and derive the charged and
two-photon neutral AGCs. We derive the general perturbative contributions to
the pure field-strength operators from spin 0, 1/2, 1 resonances by means of
the heat kernel method. In the composite Higgs framework, we derive the pattern
of expected deviations from typical SO(N) embeddings of the light composite top
partner. We then study a generic warped extra dimension framework with AdS_5
background, recasting in few parameters the features of models relevant for
AGCs. We also present a detailed study of the latest bounds from electroweak
and Higgs precision observables, with and without brane kinetic terms. For
vanishing brane kinetic terms, we find that the S and T parameters exclude KK
gauge modes of the RS custodial [non-custodial] scenario below 7.7 [14.7] TeV,
for a brane Higgs and below 6.6 [8.1] TeV for a Pseudo Nambu-Goldstone Higgs,
at 95% CL. These constraints can be relaxed in presence of brane kinetic terms.
The leading AGCs are probing the KK gravitons and the KK modes of bulk gauge
fields in parts of the parameter space. In these scenarios, the future CMS and
ATLAS forward proton detectors could be sensitive to the effect of KK gravitons
in the multi-TeV mass range.
