  New high-resolution observations reveal that small-scale magnetic flux
concentrations have a delicate substructure on a spatial scale of 0.1''. Its
basic structure can be interpreted in terms of a magnetic flux sheet or tube
that vertically extends through the ambient weak-field or field-free atmosphere
with which it is in mechanical equilibrium. A more refined interpretation comes
from new three-dimensional magnetohydrodynamic simulations that are capable of
reproducing the corrugated shape of magnetic flux concentrations and their
signature in the visible continuum. Furthermore it is shown that the
characteristic asymmetric shape of the contrast profile of facular granules is
an effect of radiative transfer across the rarefied atmosphere of the magnetic
flux concentration. I also discuss three-dimensional radiation
magnetohydrodynamic simulations of the integral layers from the top of the
convection zone to the mid-chromosphere. They show a highly dynamic
chromospheric magnetic field, marked by rapidly moving filaments of stronger
than average magnetic field that form in the compression zone downstream and
along propagating shock fronts. The simulations confirm the picture of flux
concentrations that strongly expand through the photosphere into a more
homogeneous, space filling chromospheric field. Future directions in the
simulation of small-scale magnetic fields are indicated by a few examples of
very recent work.
