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We point out the difficulties in carrying out direct numerical simulation ofthe solar dynamo problem and argue that kinematic mean-field models are ourbest theoretical tools at present for explaining various aspects of the solarcycle in detail. The most promising kinematic mean-field model is the fluxtransport dynamo model, in which the toroidal field is produced by differentialrotation in the tachocline, the poloidal field is produced by theBabcock--Leighton mechanism at the solar surface and the meridional circulationplays a crucial role. Depending on whether the diffusivity is high or low,either the diffusivity or the meridional circulations provides the maintransport mechanism for the poloidal field to reach the bottom of theconvection zone from the top. We point out that the high-diffusivity fluxtransport dynamo model is consistent with various aspects of observationaldata. The irregularities of the solar cycle are primarily produced byfluctuations in the Babcock--Leighton mechanism and in the meridionalcirculation. We summarize recent work on the fluctuations of meridionalcirculation in the flux transport dynamo, leading to explanations of suchthings as the Waldmeier effect.

Flux-transport and mean-field dynamo theories of solar cycles