  Helicity, a measure of the breakage of reflectional symmetry and a
representative of topological properties of turbulent flows, can contribute in
a crucial way to their dynamics and to their fundamental statistical
properties. We review here a few of these features, both new and old, as the
discovery of bi-directional (dual) cascades, or the role of helical vortices in
the enhancement of large-scale magnetic fields in the dynamo problem. The
dynamical contribution of the cross-correlation between the velocity and
magnetic fields in magnetohydrodynamic (MHD) is discussed as well. We consider
next how turbulent transport is affected by helical constraints, in particular
in the context of magnetic reconnection and fusion plasmas. Important issues on
how to construct turbulence models for non-reflectionally symmetric helical
flows are reviewed, including in the presence of shear, and we finally briefly
mention the role of helicity in the development of possibly-singular
structures.
