I present proper motions (tangential velocities) for the Large & Small Magellanic Clouds (LMC & SMC) based on three epochs of Hubble Space Telescope data, spanning a 7 year baseline, and centered on background quasars. The Magellanic Clouds are two of the largest and most prominent dwarf galaxies associated with the Milky Way. In addition to their velocities, the high quality of the data has allowed us to measure the rotation curve of the LMC and to constrain all aspects of its geometry purely from the proper motion data, without the need to rely on line-of-sight velocity studies. This is the first time that this has been done for an external galaxy using only optical proper motion techniques, and shows the power of upcoming time-domain surveys such as LSST. This work is part of a larger effort towards 6-D mapping of the Milky Way.