  We analyse the constraints on models of WIMP Dark Matter that can be derived
from upper bounds on the "monojet" cross section at the LHC. These constraints
were originally interpreted in the context of an effective field theory (EFT)
where the Standard Model is extended by a dimension--6 operator whose
coefficient is $1/\Lambda^2$. We show that combining the 8 TeV data of the
ATLAS and CMS collaborations improves the bounds only slightly. We then analyze
this final state in the context of simplified models with $s-$channel mediator.
We show that if the decay width of the mediator is small, these simplified
models can be accurately modeled by the effective field theory only if the
mediator mass is above 5 TeV. Finally, we point out that even if the EFT
accurately describes the ${\cal O}(\Lambda^{-2})$ contributions to the matrix
element, for values of $\Lambda$ near the current bound it receives significant
contributions of order $\Lambda^{-4}$, in the context of simplified models,
these correspond to diagrams where two mediators are exchanged. This
observation challenges the internal consistency of the EFT description since
dimension$-8$ operators, which would also contribute to ${\cal
O}(\Lambda^{-4})$ to the matrix element, are not included.
