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Abstract
The Sun's magnetic field is the engine and energy source driving all phenomena collectively defining solar activity, which in turn structures the whole heliosphere and significantly impacts Earth's atmosphere down at least to the stratosphere. The solar magnetic field is believed to originate through the action of a hydromagnetic dynamo process operating in the Sun's interior, where the strongly turbulent environment of the convection zone leads to flow-field interactions taking place on an extremely wide range of spatial and temporal scales. Following a necessarily brief observational overview of the solar magnetic field and its cycle, this review on solar dynamo theory is structured around three areas in which significant advances have been made in recent years: (a) global magnetohydrodynamical simulations of convection and magnetic cycles, (b) the turbulent electromotive force and the dynamo saturation problem, and (c) flux transport dynamos, and their application to model cycle fluctuations and grand minima and to carry out cycle prediction.