This is a comprehensive review of the uses of potential theory in
studying the spectral theory of orthogonal polynomials. Much of the article
focuses on the Stahl--Totik theory of regular measures, especially the case
of OPRL and OPUC. Links are made to the study of ergodic Schrödinger
operators where one of our new results implies that, in complete generality,
the spectral measure is supported on a set of zero Hausdorff dimension
(indeed, of capacity zero) in the region of strictly positive Lyapunov
exponent. There are many examples and some new conjectures and indications
of new research directions. Included are appendices on potential theory and
on Fekete--Szegő theory.