In several different astrophysical fields it is useful to understand the basic physics question of what happens when a disk accretes onto a binary system.  Not only is the accretion rate modulated by the presence of a binary in interesting ways, but torques between the binary and the accretion disk can determine the orbital evolution of the binary system.  In this talk, we will explore the fundamental problem of binary accretion, primarily relying on numerical models evolving the equations of hydrodynamics.  We will consider astrophysical applications in the formation of directly-observable binary star systems, as well as the evolution of supermassive black hole binaries at the cores of recently-merged galaxies, detectable in the EM via quasar variability, and in gravitational waves using pulsar timing arrays (PTAs) and eventually LISA.