The Large Magellanic Cloud (LMC), the most massive satellite of the Milky Way (MW), is perturbing the dynamics and equilibrium of the MW. Understanding the nature and time evolution of these perturbations remains one of the most important challenges to the interpretation of 6D phase space measurements of tracers (satellites, streams, halo stars) of the DM distribution and assembly history of the MW. Using results from high-resolution N-body simulations, I will describe the two main perturbations caused by the LMC: the DM wake and the barycenter displacement. Furthermore, I will illustrate how the time-dependent potential of the MW-LMC system can be modelled using Basis Function Expansions. Finally, I will discuss how some current challenges to cold dark matter theory, such as the plane of satellites of the MW, are likely natural consequences of the MW-LMC interaction.