The Sun's magnetic surface The magnetic field of the Sun is generated in its convective envelope. It is often considered a manifestation of 'the interaction between magnetic fields and turbulent convection'. In the first part of the talk I'll review some observations, old and new, which show that such a turbulent interaction picture fits the observations poorly. The observations, complemented with numerical work, lead to a considerably different conceptual picture of the solar cycle. In a second part I briefly review some spectacular recent successes in realistic numerical simulations of magnetic structures at the solar surface, which have greatly boosted confidence in our ability to reproduce observables with realistic radiative MHD simulations. In the third I discuss the (controversial) possibility that variations of the Sun's magnetic field might have an influence on climate.