The solar magnetic field drives a wide range of phenomena, from sunspots to flares and coronal mass ejections. This field is maintained against ohmic dissipation by means of a hydromagnetic dynamo. In recent years, evidence has accumulated in support of a particular family of dynamo models, Babcock-Leighton models, where the surface fields play a key role. Specifically, the surface transport of magnetic flux coming from emerged regions regenerates the global dipole field, which is the source of the subsurface toroidal field for the next cycle.
Many global dynamo models rely on the approximation of axial symmetry. In this thesis, we explore the consequences of relaxing this assumption. Relaxing it on the the surface, we find that the large-scale converging flows around active regions affect the strength of the global dipole. This may contribute to the variability of the solar cycle and provides a saturation mechanism. Relaxing the assumption beneath the surface, we find that the subsurface azimuthal field of the Sun is strongly axisymmetric.