Direct searches of Dark Matter aim at detecting the tiny nuclear recoils arising from non-relativistic collisions between DM particles and nuclei in underground detectors. The talk is divided in three parts where I'll present: i) the most general approach to study signals in direct searches based on non-relativistic EFT operators and interactions; ii) how to match a non-complete set of high-energy effective operators down to non-relativistic DM-nucleus interactions in order to derive bounds on the energy scale of such operators; iii) how the running of the SM couplings between the energy scale of the mass of the mediator down to the nuclear energy scale generates operator mixing and, in turn, new interactions at low-energy. The inclusion of the running is not optional and give rise to important phenomenological consequences that I'll carefully discuss