Large-scale magnetic fields of celestial bodies are thought to be generated by the joint action of differential rotation and what is generally known as the alpha-effect—associated with a violation of mirror-symmetry in rotating convection or turbulence. The Coriolis force acting on rotating vortices in a stratified media results in an excess of right-hand vortices in one hemisphere and left-hand vortices in the other. This asymmetry gives a component of the mean electromotive force parallel to the mean magnetic field (the electromotive force and the electric current are perpendicular to the magnetic field in mirror-symmetric media). This is the famous alpha-effect which plays a key role in magnetic field self-excitation (the so-called mean-field dynamo) and leads to the solar cycle and other phenomena in astrophysical plasma.A new finding in this field is that the nonlinear saturation of the dynamo instability is determined by transport properties of the magnetic helicity, which is an inviscid integral of motion and describes the mirror asymmetry of the magnetic field generated. We discuss first observational results concerning helicity transport in the solar cycle in the context of solar dynamo models.