These refereed Conference Proceedings are intended to summarise the latest developments in diffraction theory as reported at the IUTAM Symposium on Diffraction and Scattering in Fluid Mechanics and Elasticity held in Manchester, England, in July 2000.This informal meeting was organised to discuss the mathematical advances, both from the theoretical and more applied points of view; however, its primary goal was to foster interactions between scientists and engineers working with waves in fluids and waves in solids who share common models, phenomenological features arising in such problems, and common mathematical tools. The topics covered include surface water waves and other geophysical waves, diffraction and propagation of acoustic waves, trapped modes in single and multi-body problems, propagation through inhomogeneous media, elastic wave propagation and scattering including non-destructive testing, and fluid structural wave interactions.