  We discuss effective field theories (EFTs) for the Higgs particle, which is
not necessarily the Higgs of the Standard Model. We distinguish two different
consistent expansions: EFTs that describe decoupling new-physics effects and
EFTs that describe non-decoupling new-physics effects. We briefly discuss the
first case, the SM-EFT. The focus of this thesis is on the non-decoupling EFTs.
We argue that the loop expansion is the consistent expansion in the second
case. We introduce the concept of chiral dimensions, equivalent to the loop
expansion. Using the chiral dimensions, we expand the electroweak chiral
Lagrangian up to next-to-leading order,
$\mathcal{O}(f^{2}/\Lambda^{2})=\mathcal{O}(1/16\pi^{2})$.
  We then compare the decoupling and the non-decoupling EFT. We also consider
scenarios in which the new-physics sector is non-decoupling at a scale $f$, far
above the electroweak-scale $v$. We discuss the relevance of the resulting
double expansion in $\xi=v^{2}/f^{2}$ and $f^{2}/\Lambda^{2}$ for the data
analysis at the LHC.
  In the second part, we discuss the applications of the EFTs, especially of
the electroweak chiral Lagrangian. First, we connect the EFT with explicit
models of new physics. We show how different regions of the parameter space of
the same model generate a decoupling and a non-decoupling EFT.
  Second, we use the expansion at leading order to describe the current LHC
Higgs data. We show how the current parametrization of the Higgs data, the
$\kappa$-framework, can be justified quantum field theoretically by the EFT. We
fit the data of Run-1 (2010--2013). The effective Lagrangian describing this
data can be reduced to six free parameters. The result of this fit is
consistent with the SM, but it has statistical uncertainties of about ten
percent.
