  The most widely accepted model of the solar cycle is the flux transport
dynamo model. This model evolved out of the traditional $\alpha \Omega$ dynamo
model which was first developed at a time when the existence of the Sun's
meridional circulation was not known. In these models, the toroidal magnetic
field (which gives rise to sunspots) is generated by the stretching of the
poloidal field by solar differential rotation. The primary source of the
poloidal field in the flux transport models is attributed to the
Babcock--Leighton mechanism, in contrast to the mean-field $\alpha$-effect used
in earlier models. With the realization that the Sun has a meridional
circulation, which is poleward at the surface and is expected to be equatorward
at the bottom of the convection zone, its importance for transporting the
magnetic fields in the dynamo process was recognized. Much of our understanding
about the physics of both the meridional circulation and the flux transport
dynamo has come from the mean field theory obtained by averaging the equations
of MHD over turbulent fluctuations. The mean field theory of meridional
circulation makes clear how it arises out of an interplay between the
centrifugal and thermal wind terms. We provide a broad review of mean field
theories for solar magnetic fields and flows, the flux transport dynamo
modeling paradigm and highlight some of their applications to solar and stellar
magnetic cycles. We also discuss how the dynamo-generated magnetic field acts
on the meridional circulation of the Sun and how the fluctuations in the
meridional circulation, in turn, affect the solar dynamo. We conclude with some
remarks on how the synergy of mean field theories, flux transport dynamo
models, and direct numerical simulations can inspire the future of this field.
