Theoretical models for Dark Matter

WIMP paradigm is an attractive solution for the Dark Matter puzzle in view of the production mechanism, only driven by particle physics inputs, and by the broad variety of experimental tests available. The many different experimental searches makes crucial the presence of an efficient interface between experimental outcome and theory. This kind of interface has been provide firstly by Effective field Theories and, at later times, by the so called “Simplified Models”. I will provide a critical overview of these models showing from on side how they result successful in the description of the experimental outcome but discussing at the same time their limitations and possible loopholes. In the second part of the talk I will show, through some examples, the phenomenological impact from considering better theoretically motivated setups