In this talk I will present and review recent N-body simulations of the interaction of the Sgr dwarf with the Milky Way. These show for the first time a comprehensive picture in which the Sgr's repeated impacts have affected the disc in a remarkable way from its outer edges all the way to the solar-neighbourhood. I will show that the Sgr impact model naturally produces similar spiral phase-space patterns seen in the Gaia volume in (vz,z), ridges in azimuthal velocity as a function of Galactocentric radius as well as a warped and corrugated outer disc with similar amplitudes as seen in the data as well as the substructures seen towards the Galactic Anticenter (Monoceros, ACS, TriAnd). I will discuss the origins of all these structures with respect to the orbital mass-loss history of Sgr and highlight the roles of the dark matter halo wake excited by Sgr in the MW halo as well as its tides. I will discuss a number of disagreements in the models with the data and identify areas where further work should be carried out and give a vision for the near future.