Astrophysical accretion disks are powered by the release of gravitational p
otential energy as gas spirals down onto a compact star or black hole. The
dynamics and evolution of accretion disks depend upon how angular momentum
is transported outward from one fluid element to another. The nature of thi
s process was unclear for many years. Since the early 1990s, however, consi
derable progress has been made in understanding how turbulence arises and t
ransports angular momentum in astrophysical accretion disks. Accretion disk
s are generally highly conducting plasmas; the equations governing their ev
olution are those of ideal magnetohydrodynamics. Although a hydrodynamical
disk would be locally stable, the combination of a weak subthermal magnetic
field and outwardly decreasing differential rotation rapidly generates mag
netohydrodynamical turbulence via a remarkably simple linear instability. T
hus, turbulent accretion disks are fundamentally magnetohydrodynamical in n
ature. (C) 1999 American Institute of Physics. [S1070-664X(99)03512-0].