Our knowledge of the structure and dynamics of galaxies and star clusters in the Local Group has long been limited by the difficulty of
measuring velocities perpendicular to the line of sight. This is now changing due to the angular resolution and stability available with
the Hubble Space Telescope (HST). Our HST Proper Motion collaboration (HSTPROMO) has developed techniques that reach unprecedented proper motion (PM) accuracies. We have used these over the past decade to pursue many different projects. I will review our results on a range of topics, including: the dynamics of globular clusters and the possible presence of intermediate-mass black holes; the structure and shape of the Milky Way halo from PM measurements of stars in the distant metal-poor halo and the Sagittarius Stream; the mass of the Milky Way from PM measurements of the distant satellite Leo I and other dwarf galaxies; the structure and dynamics of the LMC disk from measurements of its PM rotation curve; the past and future relative orbits of the Milky Way, LMC, M31, and M33 calculated based on their measured PMs; and the inter-actions between these galaxies based on N-body calculations. These results are reshaping our understanding of the Local Group.