Winds link the supermassive black holes at the heart of active galactic nuclei (AGN) to their environment. Combined high-resolution UV and X-ray spectroscopy is a crucial tool to advance our understanding of the origin and role of these outflows in AGN. I present results from recent studies investigating the physical connection between different forms of outflows that have been found in AGN. I review the UV perspective of warm-absorber outflows, transient obscuring winds, and the ultra-fast outflows (UFOs) using spectroscopy with the Hubble Space Telescope (HST). By deciphering their variability, and mapping their ionization and kinematic structure, new insights are gained on the formation and driving of the AGN outflows.