Phononics is an emerging field focused on controlling elastic and acoustic waves across different frequency regimes to trigger exotic responses in a broad scope of applications, including sound attenuation with lightweight structures, vibration control, shock absorption, wave guiding, stabilization of flow perturbations, and thermal transport at the nanometric scale, among others. Metamaterials are artificially engineered to realize such responses, through specific topological design of their inner structures. The inherent complexity associated with metamaterials usually requires the use and development of new advanced computational techniques to model and simulate their behaviour, and to optimize their design for specific applications. These techniques include structural and fluid dynamic simulations combined with homogenization, optimization and machine learning methods, addressing challenges like eigenvalue problems and model order reduction for complex systems. This minisymposium aims to discuss topics related with metamaterials and phononic structures for any kind of application, focusing on challenges and innovations in modelling, simulation or design of such materials. Discussions may extend beyond computational aspects to explore metamaterials’ exotic properties, applications, or manufacturing challenges. The following topics fall within the scope of the minisymposium: - Modelling and design of acoustic and elastic metamaterials for sound and vibration mitigation. - Modelling and design of architected materials for tailored mechanical response and energy dissipation (mechanical metamaterial, lattice-based structures, etc.). - Modelling and design of phononic subsurfaces and metamaterials for flow manipulation (applications in pipelines, lifting bodies, wind turbines, etc.). - Modelling and design of metamaterials and phononic structures at micro and nanoscales (applications in waveguiding, thermal transport, etc.). - Reduced-order and multi-scale modelling, optimization techniques and AI-driven design of metamaterials and phononic structures. - Band structure analysis, novel applications and addressing manufacturing challenges in the field of phononics and metamaterials.