It was just over ten years ago, at Aspeniisgarden near Gothenburg, Sweden, that Pro- fessor Alexandr Sergeevich Davydov presented his soliton theory for the storage and transport of biological energy in protein to scientists from Europe, North America and Japan. Since then, his ideas have been vigorously studied and investigated throughout the world. Many feel that Davydov's theory is an important contribution to biomolecu- lar dynamics, but others caution that neglected dispersive effects may destroy the energy localization that arises ill his theory. It was to discuss these differences of opinion that we organized a NATO Advanced Research Workshop on "Self-trapping of Vibrational Energy in Protein" from July 30 to August 5, 1989 at Hanstholm, Denmark. In addition to substantial financial support from the Special Programme on "Chaos; Order and Patterns" of the NATO Scientific Affairs Division, we received it generous grant from the Danish Natural Science Research Council. We also acknowledge invalu- able assistance provided by the interdepartmental center of nonlinear studies ("MIDIT" is the Danish acronym) as well as the Laboratory of Applied Mathematical Physics, both at the Technical University of Denmark. It is a particular pleasure to thank Lise Gudmandsen and Dorthe Th[gersen for many forms of assistance before, during, and after the workshop.