The main Features of the phenomenology of WIMP dark matter candidates, as well a broad range of related processes testable at collider, can be described by simple Extension of the Standard Model by a DM candidate and a mediator of its interactions. I will show, mainly focusing on the case of fermionic DM with spin 1 mediator, how combining constraints from different dark matter search strategies can provide hints on the structure of These theories. I will also discuss possible theoretical embeddings of These simplified Setups and how current constraints and future Signals can be used to discriminate different theoretical Frameworks.