In these proceedings we review the interplay between LHC searches for dark
matter and direct detection experiments. For this purpose we consider two prime
examples: the effective field theory (EFT) approach and the minimal
supersymmetric standard model (MSSM). In the EFT scenario we show that for
operators which do not enter directly direct detection at tree-level, but only
via loop effects, LHC searches give complementary constraints. In the MSSM stop
and Higgs exchange contribute to the direct detection amplitude. Therefore, LHC
searches for supersymmetric particles and heavy Higgses place constraints on
the same parameter space as direct detection.Comment: 5 pages, 3 figures, proceedings for Moriond Gravitation 201