  I provide a broad overview of the basic theoretical paradigms of black hole
accretion flows. Models that make contact with observations continue to be
mostly based on the four decade old alpha stress prescription of Shakura &
Sunyaev (1973), and I discuss the properties of both radiatively efficient and
inefficient models, including their local properties, their expected stability
to secular perturbations, and how they might be tied together in global flow
geometries. The alpha stress is a prescription for turbulence, for which the
only existing plausible candidate is that which develops from the
magnetorotational instability (MRI). I therefore also review what is currently
known about the local properties of such turbulence, and the physical issues
that have been elucidated and that remain uncertain that are relevant for the
various alpha-based black hole accretion flow models.
