This mini-symposium is intended as a forum for exchange and debate on advanced numerical methods for tackling problems in engineering and applied sciences that involve multiscale and multiphysics couplings. The aim is to bring together scientists (engineers, physicists, mathematicians) focusing on coupling techniques in numerical modelling in fields ranging from computational mechanics to acoustics, electromagnetism and computational chemistry. Papers may cover a wide range of aspects from modelling to numerical strategies. The main focus will be on computational issues and associated advanced methods, while highlighting the underlying conceptual and theoretical foundations. Application topics will include (but not be limited to): • Heterogeneous and multiscale media; • Complex materials; • Computational homogenization; • Localized phenomena and singularities; • Multilevel or multi-model strategies; • Hierarchical methods; • Multiphysics coupling algorithms; • Interface and contact problems; • …