Most of the relevant aspects of the phenomenology of Weakly Interacting Massive Dark Matter candidates (WIMPs) can be described by considering simple extensions of the Standard Model in which a Dark Matter candidate, singlet under the SM gauge group, interacts  with the SM states through a mediator. These classes of simplified models are very manageable in view of the low amount of free parameters. At the same time they offer, nonetheless, a broad phenomenology ranging from DM Direct/Indirect detection to collider searches of both visible and invisible decay channels of the mediator. I will discuss, in some definite examples, as the combination of the constraints from different search strategies can already provide definite indications on the structure of these models. I will also briefly discuss possible embedding of this simple setups in theoretically motivated frameworks.