I discuss the dynamical interactions between the Milky Way and its satellite galaxies, focusing on the closest and most massive satellites - the Large Magellanic Cloud (LMC) and the Sagittarius dwarf galaxy. The former just has had its first close encounter with the Milky Way very recently, and the latter has been orbiting our Galaxy for several Gyr and is tidally disrupting, leaving a prominent tidal stream spanning the entire sky. Thanks to the abundant and precise observational data from the Gaia satellite and various spectroscopic surveys, we now have a very detailed view of the Sagittarius stream and the remnant. It appears that to reproduce its observed properties, one needs to take into account the gravitational effect of the LMC itself and the effect that it produces on the motion of the Milky Way: an intricate dance of three galaxies. The LMC also affects the motion of other streams and satellite galaxies in the outskirts of the Milky Way, and I discuss an approach for compensating these perturbations in the context of dynamical modelling of the Milky Way mass distribution and the analysis of satellite orbits.