This White Paper explores advances in the study of Active Galaxies which will be enabled by new observing capabilities at MeV energies (hard X-rays to gamma-rays; 0.1-1000 MeV), with a focus on multi-wavelength synergies. This spectral window, covering four decades in energy, is one of the last frontiers for which we lack sensitive observations. Only the COMPTEL mission, which flew in the 1990s, has significantly probed this energy range, detecting a handful of AGN. In comparison, the currently active Fermi Gamma-ray Space Telescope, observing at the adjacent range of 0.1-100 GeV, is 100-1000 times more sensitive. This White Paper describes advances to be made in the study of sources as diverse as tidal disruption events, jetted AGN of all classes (blazars, compact steep-spectrum sources, radio galaxies and relics) as well as radio-quiet AGN, most of which would be detected for the first time in this energy regime. New and existing technologies will enable MeV observations at least 50-100 times more sensitive than COMPTEL, revealing new source populations and addressing several open questions, including the nature of the corona emission in non-jetted AGN, the precise level of the optical extragalactic background light, the accretion mode in low-luminosity AGN, and the structure and particle content of extragalactic jets.