  In this paper, written as a general historical and technical introduction to
the various review papers collected in the special issue ``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 magnethydrodynamical 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.
