  Leptonic signatures of Dark Matter (DM) are one of the cleanest ways to
discover such a secluded form of matter at high energy colliders. We explore
the full parameter space relevant to multi-lepton (2- and 3-lepton) signatures
at the Large Hadron Collider (LHC) from representative minimal consistent
models with scalar and fermion DM. In our analysis, we suggest a new
parametrisation of the model parameter spaces in terms of the DM mass and mass
differences between DM and its multiplet partners. This parametrisation allows
us to explore properties of DM models in their whole parameter space. This
approach is generic and quite model-independent since the mass differences are
related to the couplings of the DM to the Standard Model (SM) sector. We
establish the most up-to-date LHC limits on the inert 2-Higgs Doublet Model
(i2HDM) and Minimal Fermion DM (MFDM) model parameter spaces, by using the
complementary information stemming from 2- and 3-lepton signatures. We provide
a map of LHC efficiencies and cross-section limits for such 2- and 3-lepton
signatures allowing one to easily make model-independent reinterpretations of
LHC results for analogous classes of models. We also present combined
constraints from the LHC, DM relic density and direct search experiments
indicating the current status of the i2HDM and MFDM model.
