  The turbulent cross helicity is directly related to the coupling coefficients
for the mean vorticity in the electromotive force and for the mean
magnetic-field strain in the Reynolds stress tensor. This suggests that the
cross-helicity effects are important in the cases where global inhomogeneous
flow and magnetic-field structures are present. Since such large-scale
structures are ubiquitous in geo/astrophysical phenomena, the cross-helicity
effect is expected to play an important role in geo/astrophysical flows. In the
presence of turbulent cross helicity, the mean vortical motion contributes to
the turbulent electromotive force. Magnetic-field generation due to this effect
is called the cross-helicity dynamo. Several features of the cross-helicity
dynamo are introduced. Unlike the case in the helicity or $\alpha$ effect,
where ${\bf{J}}$ is aligned with ${\bf{B}}$ in the turbulent electromotive
force, we in general have a finite mean-field Lorentz force ${\bf{J}} \times
{\bf{B}}$ in the cross-helicity dynamo. This gives a distinguished feature of
the cross-helicity effect. By considering the effects of cross helicity in the
momentum equation, we see several interesting consequences of the effect.
Turbulent cross helicity coupled with the mean magnetic shear reduces the
effect of turbulent or eddy viscosity. Flow induction is an important
consequence of this effect. One key issue in the cross-helicity dynamo is to
examine how and how much cross helicity can be present in turbulence. On the
basis of the cross-helicity transport equation, its production mechanisms are
discussed. Some recent developments in numerical validation of the basic notion
of the cross-helicity dynamo are also presented.
