Evolution of Solar and Stellar Dynamo Theory

In this paper, written as a general historical and technical introduction to the various contributions of the collection "Solar and Stellar Dynamo: A New Era", we review the evolution and current state of dynamo theory and modelling, with emphasis on the solar dynamo. Starting with a historical survey, we then focus on a set of "tension points" that are still left unresolved despite the remarkable progress of the past century. In our discussion of these tension points we touch upon the physical well-posedness of mean-field electrodynamics; constraints imposed by magnetic helicity conservation; the troublesome role of differential rotation; meridional flows and flux transpost dynamos; competing inductive mechanisms and Babcock-Leighton dynamos; the ambiguous precursor properties of the solar dipole; cycle amplitude regulation and fluctuation through nonlinear backreaction and stochastic forcing, including Grand Minima; and the promises and puzzles offered by global magnetohydrodynamical numerical simulations of convection and dynamo action. We close by considering the potential bridges to be constructed between solar dynamo theory and modelling, and observations of magnetic activity in late-type stars.