We outline and investigate a set of benchmark simplified models with the aim of providing a minimal simple framework for an interpretation of the existing and forthcoming searches of dark matter particles at the LHC. The simplified models we consider provide microscopic QFT descriptions of interactions between the Standard Model partons and the dark sector particles mediated by the four basic types of messenger fields: scalar, pseudoscalar, vector and axial-vector. Our benchmark models are characterized by four to five parameters, including the mediator mass and width, the dark matter mass and the effective coupling(s). In the gluon fusion production channel we resolve the top quark in the loop and compute full top-mass effects for scalar and pseudoscalar messengers. We show the LHC limits and reach at 8 and 14 TeV for models with all four messenger types. We also outline the complementarity of direct detection, indirect detection and LHC bounds for dark matter searches. Finally, we investigate the effects which arise from extending the simplified model to include potential new physics contributions in production. Using the scalar mediator as an example, we study the impact of heavy new physics loops which interfere with the top-mediated loops. Our computations are performed within the MCFM framework, and we provide fully flexible public Monte Carlo implementation.