Could a light Higgs boson illuminate the dark sector?

The impact a new neutral light particle of spin 0, 1/2, 1, or 3/2 could have on the tiny width of a light Higgs boson is systematically analyzed. To this end, we include all the relevant effective interactions, whether renormalizable or not, and review the possible signatures in the Higgs decay modes with missing energy. This includes the fully invisible Higgs boson decay, as well as modes with standard model gauge bosons or fermions in the final state. In many cases, simply preventing these modes from being dominant suffices to set tight model-independent constraints on the masses and couplings of the new light states.