Dark Matter through the 125 GeV Higgs window

Plenary talk at DM@LHC2018 in Heidelberg. Instructions from the organizers: "The contribution should highlight new directions in dark matter searches at ATLAS and CMS using the 125 GeV Higgs boson in Higgs-portal scenarios where the Higgs boson decays invisibly into dark matter particles. Given the expert audience of the workshop, the contribution should focus on experimental limitations of the current results and highlight non-trivial improvements of the current and future analyses (as opposed to an overview of all possible signatures and detailed descriptions of the individual analyses at ATLAS and CMS). It would be great if analysis aspects that would significantly benefit from a better theoretical description could be identified."