  After emerging to the solar surface, the Sun's magnetic field displays a
complex and intricate evolution. The evolution of the surface field is
important for several reasons. One is that the surface field, and its dynamics,
sets the boundary condition for the coronal and heliospheric magnetic fields.
Another is that the surface evolution gives us insight into the dynamo process.
In particular, it plays an essential role in the Babcock-Leighton model of the
solar dynamo. Describing this evolution is the aim of the surface flux
transport model. The model starts from the emergence of magnetic bipoles.
Thereafter, the model is based on the induction equation and the fact that
after emergence the magnetic field is observed to evolve as if it were purely
radial. The induction equation then describes how the surface flows --
differential rotation, meridional circulation, granular, supergranular flows,
and active region inflows -- determine the evolution of the field (now taken to
be purely radial). In this paper, we review the modeling of the various
processes that determine the evolution of the surface field. We restrict our
attention to their role in the surface flux transport model. We also discuss
the success of the model and some of the results that have been obtained using
this model.
