  Higgs-portal effective field theories are widely used as benchmarks in order
to interpret collider and astroparticle searches for dark matter (DM)
particles. To assess the validity of these effective models, it is important to
confront them to concrete realizations that are complete in the ultraviolet
regime. In this paper, we compare effective Higgs-portal models with scalar,
fermionic and vector DM with a series of increasingly complex realistic models,
taking into account all existing constraints from collider and astroparticle
physics. These complete realizations include the inert doublet with scalar DM,
the singlet-doublet model for fermionic DM and models based on spontaneously
broken dark SU(2) and SU(3) gauge symmetries for vector boson DM. We also
discuss the simpler scenarios in which a new scalar singlet field that mixes
with the standard Higgs field is introduced with minimal couplings to
isosinglet spin--$0, \frac12$ and 1 DM states. We show that in large regions of
the parameter space of these models, the effective Higgs-portal approach
provides a consistent limit and thus, can be safely adopted, in particular for
the interpretation of searches for invisible Higgs boson decays at the LHC. The
phenomenological implications of assuming or not that the DM states generate
the correct cosmological relic density are also discussed.
