We explore the hypothesis that dark matter couples to visible particles via the Higgs boson. Fundamental interactions with the Higgs boson are strongly constrained, because we have not observed nucleon scattering in direct detection experiments. Viable models therefore often require additional particles in the dark sector. This implies a rich phenomenology, which can be tested at current collider and direct detection experiments. In this talk, the focus will be on scenarios with very weak Higgs interactions, which predict signatures with long-lived mediators at the LHC. I will show that their discovery might reveal how the dark matter abundance has been produced in the early universe.