Recent high-resolution observations of the surface of the Sun have revealed the fine structure of a vast array of complex photospheric magnetic features. Observations of these magnetic field structures have already greatly enhanced our theoretical understanding of the interactions between magnetic fields and turbulent convection, and future photospheric observations will inevitably present new theoretical challenges. In this review, I discuss recent progress that has been made in the modelling of photospheric magnetic fields. In particular, I focus upon the complex field structures that are observed within the umbrae and the penumbrae of sunspots. On a much smaller scale, I also discuss models of the highly localized magnetic field structures that are observed in less magnetically active regions of the photosphere. As the spatial resolution of telescopes has improved over the last few years, it has now become possible to observe these features in detail, and theoretical models can now describe much of this behaviour. In the last section of this review, I discuss some of the remaining unanswered questions.
Evolution of localized magnetic field perturbations and the nature of turbulent dynamo