  Convectively driven dynamos with rotation generating magnetic fields on
scales large compared with the scale of the turbulent eddies are being
reviewed. It is argued that such fields can be understood as the result of an
alpha effect. Simulations in Cartesian domains show that such large-scale
magnetic fields saturate on a time scale compatible with the resistive one,
suggesting that the magnitude of the alpha effect is here still constrained by
approximate magnetic helicity conservation. It is argued that, in the absence
of shear and/or any other known large-scale dynamo effects, these simulations
prove the existence of turbulent alpha^2-type dynamos. Finally, recent results
are discussed in the context of solar and stellar dynamos.
