The fundamental problem in deriving energy from accretion onto black

holes is the nature of angular momentum transport. Strong arguments

link this process to MHD turbulence driven by the magneto-rotational instability.

Using large-scale numerical simulations that include full general relativity, it is now

possible to trace MHD turbulence and the resulting accretion dynamics in

considerable detail. These simulations have enriched our understanding of

black hole accretion flows and changed long-standing views about them. Contrary

to the central guess of the Novikov-Thorne model, magnetic stresses persist throughout

the flow, and are particularly strong when the black hole rotates rapidly. With

toy-model cooling functions, we can now calculate directly the radiation arriving

at infinity; due to these additional stresses, the radiative efficiency can be

greater than the classical prediction. When the internal magnetic field topology

is appropriate, large-scale magnetic field can be spontaneously generated in a cone

around the rotation axis, creating a relativistic Poynting-dominated jet

whose strength increases sharply with increasing black hole spin. Lastly,

contrary to a prediction of the Shakura-Sunyaev alpha model, the inner portions

of bright disks around black holes, where radiation pressure dominates, are

thermally stable.