Advances in mean-field dynamo theories

We give a short introduction to the subject and review advances in understanding the basic ingredients of the mean-field dynamo theory. The discussion includes the recent analytic and numerical work in developments for the mean electromotive force of the turbulent flows and magnetic field, the nonlinear effects of the magnetic helicity, the non-local generation effects in the dynamo. We give an example of the mean-field solar dynamo model that incorporates the fairly complete expressions for the mean-electromotive force, the subsurface shear layer and the conservation of the total helicity. The model is used to shed light on the issues in the solar dynamo and on the future development of this field of research.