The modern understanding of turbulence is that it is a collection of weakly correlated vortical motions, which, despite their intermittent and chaotic distribution over a wide range of space and time scales, actually consist of local characteristic 'eddy' patterns that persist as they move around under the influences of their own and other eddies' vorticity fields. Numerical simulations and experimental observations have now identified some forms and elements of 'life-cycles' of some of these structures. The articles in this volume, first published in 2000, examine a number of key questions that have engaged turbulence researchers for many years. Most involve mathematical analysis, but some describe numerical simulations and experimental results that focus on these questions. However, all are addressed to a wide cross-section of the turbulence community, namely mathematicians, engineers and scientists.