The solar dynamo: old, recent, and new problems

A number of problems of solar and stellar dynamo theory are briefly reviewed and the current status of possible solutions is discussed. Results of direct numerical simulations are described in view of mean-field dynamo theory and the relation between the alpha-effect and the inverse cascade of magnetic helicity is highlighted. The possibility of `catastrophic' quenching of the alpha-effect is explained in terms of the constraint placed by the conservation of magnetic helicity.