  Collider experiments are one of the most promising ways to constrain Dark
Matter (DM) interactions. For several types of DM-Standard Model couplings, a
meaningful interpretation of the results requires to go beyond effective field
theory, considering simplified models with light mediators. This is especially
important in the case of loop-mediated interactions. In this paper we perform
the first simplified model study of the magnetic dipole interacting DM, by
including the one-loop momentum-dependent form factors that mediate the
coupling -- given by the Dark Penguin -- in collider processes. We compute
bounds from the monojet, monophoton, and diphoton searches at the $8$ and $14$
TeV LHC, and compare the results to those of direct and indirect detection
experiments. Future searches at the $100$ TeV hadron collider and at the ILC
are also addressed. We find that the optimal search strategy requires loose
cuts on the missing transverse energy, to capture the enhancement of the form
factors near the threshold for on-shell production of the mediators. We
consider both minimal models and models where an additional state beyond the DM
is accessible. In the latter case, under the assumption of anarchic flavor
structure in the dark sector, the LHC monophoton and diphoton searches will be
able to set much stronger bounds than in the minimal scenario. A determination
of the mass of the heavier dark fermion might be feasible using the $M_{T2}$
variable. In addition, if the Dark Penguin flavor structure is almost aligned
with that of the DM mass, a displaced signal from the decay of the heavier dark
fermion into the DM and photon can be observed. This allows us to set
constraints on the mixings and couplings of the model from an existing search
for non-pointing photons.
