Equilibrium measures and capacities in spectral theory

This is a comprehensive review of the uses of potential theory instudying the spectral theory of orthogonal polynomials. Much of the articlefocuses on the Stahl--Totik theory of regular measures, especially the caseof OPRL and OPUC. Links are made to the study of ergodic Schrödingeroperators 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 Lyapunovexponent. There are many examples and some new conjectures and indicationsof new research directions. Included are appendices on potential theory andon Fekete--Szegő theory.