  We discuss some aspects of dark matter phenomenology, in particular related
to Direct detection and collider searches, of models in which a fermionic Dark
Matter interacts with SM fermions through spin 1 mediators. Contrary to
conventional simplified models we will consider fixed assignments of the
couplings of the ($Z^{'}$) mediator, according theoretically motivated
embeddings. This allows to predict signals at future experimental facilities
which can be used to test and possibly discriminate different realizations.
