Tracking the 3-dimensional motions of stars in nearby galaxies is a recent astronomical breakthrough that has substantially increased our knowledge of how galaxies grow, evolve, and interact with each other over cosmic time. My research focuses on using such measurements to understand the history of the Local Group, which is composed of our Milky Way, its twin galaxy, Andromeda, and the dozens of small "satellite" galaxies orbiting around each of them. These dynamical measurements now make it possible to trace the orbital histories of Local Group galaxies to their origins in the early Universe. In my work, I use the combined power of these observational data sets with data from high-resolution simulations of the Universe to uncover the dynamical history and future fate of our galactic neighborhood.