In this talk we introduce the field of General Relativistic Magnetohydrodynamics (GRMHD) and give an overview on recent efforts toward simulating and visualizing astrophysically realistic gas dynamics around compact binaries. In particular we motivate the approach where a post-Newtonian expansion is used to construct an analytic spacetime, and show preliminary results of circumbinary disks surrounding equal-mass non-spinning black hole binaries.