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: () global magnetohydrodynamical simulations of convection and magnetic cycles, () the turbulent electromotive force and the dynamo saturation problem, and () flux transport dynamos, and their application to model cycle fluctuations and grand minima and to carry out cycle prediction.

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    Magnetic cycles in a global EULAG-MHD anelastic simulation, essentially identical to those by Ghizaru et al. (2010) and Racine et al. (2011). This simulation includes a convectively stable fluid layer underlying the convecting layers. () A snapshot in Mollweide projection of the toroidal (zonal) magnetic component at depth /R=0.718; () a snapshot of the zonally averaged toroidal field in a meridional plane taken at the same time as panel . () Time-latitude and () radius-latitude diagrams of the zonally averaged toroidal field, the former at depth /R=0.718 and the latter at latitude +25°. The dashed lines in panels and indicate the bottom of the convectively unstable layers. This is a moderate-resolution simulation, rotating at the solar rate but subluminous with respect to the Sun.

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