Twentyfirst Arnold Sommerfeld Lecture Series, Superconductivity, the ability of certain materials to conduct electricity with

no resistance whatsoever, has fascinated scientists since its discovery by

Kammerlingh-Onnes in 1911. While much has been understood, the question

of predicting which materials will become superconducting, and at what

temperatures, remains one of the grand challenges of modern materials

theory. This talk will outline the evolution of our understanding as the subject

has progressed from its primitive beginnings through the ''bronze age''

marked by the 1986 discovery of high temperature superconductivity in

copper-oxide compounds to the present-day ''iron age'' of the Fe-As based

superconducting materials. The current status of the theory of the origin of

superconductivity will be described.