  The theory of large scale dynamos is reviewed with particular emphasis on the
magnetic helicity constraint in the presence of closed and open boundaries. In
the presence of closed or periodic boundaries, helical dynamos respond to the
helicity constraint by developing small scale separation in the kinematic
regime, and by showing long time scales in the nonlinear regime where the scale
separation has grown to the maximum possible value. A resistively limited
evolution towards saturation is also found at intermediate scales before the
largest scale of the system is reached. Larger aspect ratios can give rise to
different structures of the mean field which are obtained at early times, but
the final saturation field strength is still decreasing with decreasing
resistivity. In the presence of shear, cyclic magnetic fields are found whose
period is increasing with decreasing resistivity, but the saturation energy of
the mean field is in strong super-equipartition with the turbulent energy. It
is shown that artificially induced losses of small scale field of opposite sign
of magnetic helicity as the large scale field can, at least in principle,
accelerate the production of large scale (poloidal) field. Based on mean field
models with an outer potential field boundary condition in spherical geometry,
we verify that the sign of the magnetic helicity flux from the large scale
field agrees with the sign of alpha. For solar parameters, typical magnetic
helicity fluxes lie around 10^{47} Mx^2 per cycle.
