Alexander Movchan is a Professor at the University of Liverpool, Natasha Movchan is a Professor at the University of Liverpool, Ian Jones is a Professor at Liverpool John Moores University and an Honorary Fellow at the University of Liverpool, and Daniel Colquitt is a Lecturer at the University of Liverpool. The authors have worked on wave propagation in multi-scale elastic media over many years and have developed novel modelling approaches, which have opened efficient ways to design and study the dynamic response of multi-scale structures known as elastic metamaterials introduced within the last decade.