How Astrophysical Black Holes Shine

The defining feature of a black hole is its event horizon through which nothing can escape outward, not even light.  And yet black holes are responsible for the brightest sources that we observe in the universe, from gamma-ray bursts to quasars. Their enormous luminosity arises from the release of gravitational binding energy outside the horizon as material falls inward.  These black hole accretion flows exhibit extraordinary behavior, including outbursts, state transitions, and quasi-periodic variability, most of which continue to defy understanding but which must be related to the magnetohydrodynamic turbulence and radioactive thermodynamics that govern the physics of these flows.  I will review recent theoretical progress in understanding this physics, much of which has been achieved through numerical simulations of the flows.