  We present accurate and up-to-date constraints on the complete set of
dimension five and six operators with scalar, fermion and vector Dark Matter
(DM). We find limits using LHC mono-jet data, spin inde- pendent and spin
dependent direct searches, relic density and CMB, and show the interplay
between high and low energy data in setting bounds on the parameter space. In
order to properly compare data taken at different energies, we take into
account the effect of the running and mixing of operators. We also take into
account the local density uncertainties affecting direct detection data, and
apply EFT validity criteria related to the cut on the invariant mass of DM pair
production at the LHC, which turns out to be especially important for the case
of vector DM. Finally, we estimate the potential of the future LHC runs to
probe DM parameter space.
