  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.
