The Kuiper belt, found beyond the orbit of Neptune, consists of a population of small, icy bodies that orbit the Sun. Due to perturbations from the giant planets (Jupiter, Saturn, Uranus, Neptune), the orbits of these objects slowly evolve with time. In this talk, we will analyze the orbital dynamics of the Kuiper belt objects (KBOs) both with numerical simulations and with a theoretical Hamiltonian approach. We will discuss the structure of the outer Solar System and focus on the most extreme sub-population of objects: the long-period high eccentricity class. The orbits of these extreme KBOs all appear to point in the same direction in physical space; this anomalous signal cannot be explained by the currently known eight-planet Solar System. In order to understand their origin and dynamics, we introduce the hypothesized Planet Nine to the distant Kuiper belt. We find that the presence of Planet Nine allows for two stable populations of objects - the aligned and anti-aligned KBOs - in agreement with observations. We will discuss the mechanisms that lead to this stability, and focus on a fascinating process called resonance hopping, in which a KBO rapidly transitions from one resonance to another with Planet Nine. By tying together studies of observed KBOs with more general analyses of the evolution of synthetic test particles, we elucidate the dynamics of the outer Solar System in and out of the Planet Nine context.