The workshop aims to advance the mathematical design and analysis of wave propagation in metamaterials and complex media for a wide variety of applications of major importance for industry and society. It will focus on two outstanding and interconnected themes of multiple wave scattering identified during the parent programme and which have rapidly progressed since: (i) heterogeneous materials with varying degrees of order/disorder, and (ii) locally resonant materials, with applications in water-wave energy harvesting, electromagnetics/optics, acoustics/elastic waves etc.