The active field of multi-phase flow has undergone fundamental changes in the last decade. Many salient complex interfacial dynamics of such flows are now understood at a basic level with precise mathematical and quantitative characterization. This is quite a departure from the traditional empirical approach. At an IUTAM Symposium at Notre Dame, in 1999, some of the leading researchers in the field gathered to review the progress thus far and to contemplate future directions. Their reports are summarized in this Proceedings. Topics covered include solitary wave dynamics on viscous film flows, sheet formation and drop entrainment in stratified flow, wetting and dewetting dynamics, self-similar drop formation dynamics, waves in bubbly and suspension flow, and bubble dynamics. It is a unique and essential reference for applied mathematicians, physicists, research engineers, and graduate students to keep abreast of the latest theoretical and numerical developments that promise to transform multi-phase flow research.