  We consider the possible existence of a SM-neutral and light dark sector
coupled to the visible sector through irrelevant portal interactions. Scenarios
of this kind are motivated by dark matter and arise in various extensions of
the Standard Model. We characterize the dark dynamics in terms of one
ultraviolet scale $\Lambda_\text{UV}$, at which the exchange of heavy mediator
fields generates the portal operators, and by one infrared scale
$\Lambda_\text{IR}$, setting the mass gap. At energies $\Lambda_\text{IR} \ll E
\ll \Lambda_\text{UV}$ the dark sector behaves like a conformal field theory
and its phenomenology can be studied model independently. We derive the
constraints set on this scenario by high- and low-energy laboratory experiments
and by astrophysical observations. Our results are conservative and serve as a
minimum requirement that must be fulfilled by the broad class of models
satisfying our assumptions, of which we give several examples. The experimental
constraints are derived in a manner consistent with the validity of the
effective field theory used to define the portal interactions. We find that
high-energy colliders give the strongest bounds and exclude UV scales up to a
few TeV, but only in specific ranges of the IR scale. The picture emerging from
current searches can be taken as a starting point to design a future
experimental strategy with broader sensitivity.
