Guided waves are one of the most efficient techniques for Structural Health Monitoring (SHM) in large-scale or slender structures, as they provide damage detection, localization and characterization capabilities across a broad range of structures and materials. Progress in the field has a direct impact on EU transportation, aerospace and offshore industries, where safety is crucial given the potential human, economic or environmental consequences of failures. Despite some encouraging applications to lightweight structures, the implementation of vibration- or wave-based SHM strategies in advanced structures remains challenging. Indeed, in order to combine high stiffness-to-weight ratio with low vibro-acoustic signatures these structures frequently involve composites, dissipative materials or periodic patterns to produce desirable response within targeted bandwidths. These new lightweight designs, metamaterials, or meta-structures also produce more complex propagative behaviors, such as mode conversions or Bragg resonances, which result in highly scattering waves and increased noise-to-signal ratios. This project aims to develop the numerical framework and physical models able to support model-based SHM and guided wave testing solutions in complex media such as acoustic metamaterials and large-scale periodic structures.