The understanding of electronic behaviour in solids when (some of) the valence electrons have both localized and band-like characteristics is one of the central problems of physics and chemistry in the second half of this century. Many advances have indeed been made using highly sophisticated techniques and concepts. Our objectives in bringing together specialists from different areas was cross-fertilization of ideas and redefinition of bottlenecks and problems. The testimony of the participants and the book which follows indicate a fair degree of success. This book is a record of discussions aimed at digestion and reassessment of some of the recent major advances in our understanding of