Direct searches for Dark Matter (DM) aim at detecting the nuclear recoils arising from a scattering between DM particles and target nuclei in underground detectors. Since the physics that describes the collision between DM particles and target nuclei is deeply non-relativistic, in the first part of this seminar I'll review a different and more general approach to study signal in direct DM searches based on non-relativistic operators. Then I'll present the main observables and the experimental landscape pointing out all the uncertainties that enter in this field. Finally, since the underlying relativistic theory that describes both the DM and standard model fields is unknown, in the last part of the seminar I'll be focussed on the uncertainties coming from the nature of the interaction. On a more specific level, it will be divided in two parts: i) a model independent part, in which I'm going to present a new framework and a self-contained set of numerical tools to the derive the bounds from some current direct detection experiments in a completely model independent way; ii) a model dependent part, in which I'll review the different phenomenology of ``non-standard'' DM models characterized by a long-range DM-nucleus interaction.