In the past few years, high-sensitivity, high-resolution, sub-millimeter imaging has provided robust statistics on disks in young binary systems, showing that both wide and close binaries possess substantial gas disks. Whether these disks have interacted or will interact during their lifetimes remains an open question. I will describe the basics of the novel, moving-mesh scheme AREPO (Springel 2010), and illustrate some of its applications to the modeling of binary star+disk systems. As a Lagrangian/Eulerian code, Arepo combines some properties of grid-based and particle-based codes, making it a promising tool for high-Mach number, geometrically complex astrophysical flows. I will show results of the first simulations of self-gravitating disk-disk interaction on a moving mesh, focusing on massive young binary systems.