I will discuss the impact of hypothetical new neutral light particles on the tiny width of a light Higgs boson. To this end, I will review the possible signatures in the Higgs decay modes with missing energy, including all the relevant effective interactions, whether renormalizable or not. This includes the fully invisible Higgs boson decay, as well as modes with SM 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. Then I will apply this analysis to Higgs portal models of dark matter (DM), where DM is light enough to contribute to invisible Higgs decays. I will show that DM can be a thermal relic only if there are additional light particles present with masses below a few 100 GeV. Three concrete examples of viable Higgs portal models of light DM will be discussed: (i) the SM extended by DM scalar along with an electroweak triplet and a singlet, (ii) a Two Higgs Doublet Model of type II with additional scalar DM, (iii) SM with DM and an extra scalar singlet that is lighter than DM. In all three examples the invisible Higgs decay constraint is not too restrictive, because it is governed by different parameters than the relic abundance. Implications of additional light particles for flavor violation and collider searches will be briefly discussed.