These refereed conference proceedings are intended to summarise contemporary developments in diffraction theory. The meeting was organised to discuss the mathematical advances, both from 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.