Magnetism is a ubiquitous feature of stars like our Sun. The magnetic fields that we observe at the surface, and the magnetic activity that heats stellar chromospheres, are driven by dynamo processes in the sub-surface stellar convection zones. Here I will talk about recent advances in global-scale 3-D MHD simulations of stellar dynamos. Convection and large-scale flows couple to build wreath-like global-scale magnetic structures in the stellar convection zones. The polarity of these magnetic fields can cyclically reverse with cycle periods of several years. For the first time in a global-scale simulation, we are now finding self-consistently generated buoyant magnetic structures: these may be a first step towards capturing the formation of active regions and sunspots within such models. I will also discuss advances in our understanding of the low-mach number fluid equations that we use in studying global stellar convection and the path forward with such global-scale simulations.
Followed by wine and cheese in Pupin 1402.