  I outline the theory of accretion onto black holes, and its application to
observed phenomena such as X-ray binaries, active galactic nuclei, tidal
disruption events, and gamma-ray bursts. The dynamics as well as radiative
signatures of black hole accretion depend on interactions between the
relatively simple black-hole spacetime and complex radiation, plasma and
magnetohydrodynamical processes in the surrounding gas. I will show how
transient accretion processes could provide clues to these interactions. Larger
global magnetohydrodynamic simulations as well as simulations incorporating
plasma microphysics and full radiation hydrodynamics will be needed to unravel
some of the current mysteries of black hole accretion.
