The Milky Way is a relatively typical galaxy, and we are in the middle of it. That allows astronomers to observe an enormous amount of individual stars and their properties. With the success of the Gaia mission, the amount of catalogued stars is reaching into the billions. Studying the dynamics of these stars helps to paint a picture of the formation history of the Milky Way in the context of physical cosmological models. These typically rely on simplifying assumptions like time-independence or symmetry. However, recent observations show that these assumptions do not hold in the actual Milky Way. In this Thesis, we discuss the dynamics of the Milky Way under the influence of time-dependent and asymmetric effects. We do this by exploring the Gaia data, and trying to replicate similar situations and observations using computer simulations. We study the effect of Milky Way satellites and its deforming dark matter halo on stellar streams, remnants of stellar clusters that disrupt due to tidal gravitational forces, and find that the morphology and dynamical properties of stellar streams can be heavily impacted due to these time-dependent effects. We study the effectiveness of the alternative gravitational model MOND in reproducing observed substructure in the Helmi streams and find that it is currently unable to explain the substructure. We also study the effectiveness of applying axisymmetric time-independent Jeans equations to the Milky Way disk, where we again find that not modelling time-dependent effects and asymmetry biases our inference of the Milky Way disk’s dynamical properties.