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-$0, \frac{1}{2}$ 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.