Explore observational tests of binary system theories in this 49-minute conference talk by Sterl Phinney from Caltech. Delve into the complex world of binary systems, from stellar pairs to supermassive black holes in galactic nuclei, and their interactions with surrounding circumbinary gas. Examine how this gas evolves and influences embedded binaries, and discover the most informative observational signatures. Learn about the latest numerical techniques used to model these systems more accurately. Part of the "Building Bridges: Towards a Unified Picture of Stellar and Black Hole Binary Accretion and Evolution" conference at the Kavli Institute for Theoretical Physics, this talk bridges the gap between massive black hole binary research and stellar binary studies, highlighting similarities across vastly different astrophysical scales and identifying crucial next steps in advancing our understanding of these fascinating systems.