  Accretion disc theory is less developed than stellar evolution theory
although a similarly mature phenomenological picture is ultimately desired.
While the interplay of theory and numerical simulations has amplified community
awareness of the role of magnetic fields in angular momentum transport, there
remains a long term challenge to incorporate insight gained from simulations
back into improving practical models for comparison with observations. Here we
emphasize the need to incorporate the role of non-local transport more
precisely. To show where large scale transport would fit into the theoretical
framework and how it is currently missing, we review why the wonderfully
practical approach of Shakura-Sunyaev (1973,SS73) is necessarily a mean field
theory, and one which does not include large scale transport. Observations of
coronae and jets combined with the interpretation of results even from shearing
box simulations of the magnetorotational instability (MRI) suggest that a
significant fraction of disc transport is indeed non-local. We show that the
Maxwell stresses in saturation are dominated by large scale contributions and
the physics of MRI transport is not fully captured by a viscosity. We also
clarify the standard physical interpretation of the MRi as it applies to
shearing boxes. Computational limitations have so far focused most attention
toward local simulations but the next generation of global simulations should
help to inform improved mean field theories. Mean field accretion theory and
mean field dynamo theory should in fact be unified into a single theory that
predicts the time evolution of spectra and luminosity from separate disc,
corona, and outflow contributions. Finally, we note that any mean field theory
has a finite predictive precision that needs to be quantified when comparing
the predictions to observations.
