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. ; Comment: 32 pages + appendices and references, 22 figures