The Large and Small Magellanic Clouds (LMC/SMC), as two of the closest and most massive satellites of the Milky Way, have significant effects on the local Universe; including on the orbits of tidal streams, and on the distribution of ultra-faint satellites. However their masses, and interaction history beyond the most recent LMC/SMC close passage, remain poorly constrained. In this presentation, I will discuss the Magellanic Edges Survey (MagES), which photometrically and kinematically maps the extremely low-surface-brightness periphery of the Clouds, in order to shed light on these issues. We present a contiguous, panoramic view of the Clouds' outskirts, obtained using the Dark Energy Camera, revealing signicant distortions to the bodies of the Clouds; together with a wealth of stellar substructure extending to distances beyond 23 degrees from the Clouds' centres. Further, we use a combination of Gaia astrometry and spectroscopically-derived radial velocities, obtained with 2dF+AAOmega on the Anglo-Australian Telescope, to determine the first 3D kinematics for these substructures. Our initial results focus on the northern LMC, where we reveal a large substructure that, due to its discrepant kinematics relative to the LMC disk, was likely formed during a recent interaction with the Milky Way. Ultimately, our survey aims to provide a new benchmark for assessing dynamical models, in order to shed light on both the origin of Magellanic substructures, and the evolution of the Magellanic/Milky Way system.