This work highlights some advances in interfacial research in the fields of fluid dynamics and materials science at the beginning of the 21st century. It is an extension of the presentations made during the conference Interfaces for the Twenty-First Century , held on 16-18 August 1999, in Monterey, California. It includes papers by 16 experts in the field of interfacial mechanics, abstracts contributed by research scientists, and a summary of a panel discussion on future research directions. The text covers experimental and theoretical approaches, with the unifying philosophy being the investigation of new techniques for modelling the dynamics of interfaces. A number of solution methods and experimental studies, as well as the physical problems that initiated them, are presented.