Dynamos and Differential Rotation: Advances at the Crossroads of Analytics, Numerics, and Observations

The recent observational, theoretical, and numerical progress made in understanding stellar magnetism is discussed. Particularly, this review will cover the physical processes thought to be at the origin of these magnetic fields and their variability, namely dynamo action arising from the interaction between convection, rotation, radiation and magnetic fields. Some care will be taken to cover recent analytical advances regarding the dynamics and magnetism of radiative interiors, including some thoughts on the role of a tachocline. Moreover, recent and rapidly advancing numerical modeling of convective dynamos will be discussed, looking at rapidly rotating convective systems, grand minima and scaling laws for magnetic field strength. These topics are linked to observations or their observational implications.