In this talk I present an overview of our recent work which aims to characterize the impact of host-satellite interactions on the observable properties of Milky Way-like galaxies and, in particular, of our own. Our goals are to characterize how often disc's corrugation patterns arise in the Local Universe and what are the main physical mechanisms driving them. We use a suite of fully cosmological high resolution simulations from the Auriga Project to analyze the present-day vertical structure of individual Milky Way-sized models. We show that, at redshift zero, about 70% of our discs show strong vertical patterns with large amplitudes. Half of these are typical `integral sign' warps. The rest are corrugation patterns, similar to those observed in the Milky Way.  These perturbations have a variety of causes such as close encounters with satellites or  accretion of misaligned cold gas from halo infall or from mergers. More interestingly, we show examples of how the halo dark matter component can react to distant fly-by interactions by developing overdensity wakes.  Finally, I will discuss the observed vertical perturbations of our Galactic disc and present detailed numerical models for its formation, based on the interaction with the Sagittarius dwarf spheroidal galaxy and the Large Magellanic Cloud.