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. Our focus will be on scenarios with very weak
Higgs interactions, which predict signatures with long-lived mediators
at the LHC. We show that their discovery might reveal how dark matter
has been produced in the early universe.