Demand for highly trained scientists with a deep understanding of wave propagation in complex media, and capable of exploiting this knowledge to develop imaging tools for seismology and acoustics, is very high in the Earth and environmental sciences. Wave-based imaging serves to map spatial and temporal variations in the structure of the Earth's interior, of the oceans and atmosphere; it is used to monitor faults and volcanoes and detect natural-resource reservoirs. It is relevant to other disciplines, medical imaging being one of its most widespread applications. Today’s Earth scientists are faced with a set of questions that require the application of wave-based imaging at unprecedented resolution. WAVES contributed to fostering scientific and technological advances in this context, stimulating knowledge exchange between seismologists and acousticians, and researchers in the public/private domains. Through WAVES, a new, unique international network of scientists has been created around a set of novel physical acoustics laboratories (managed by beneficiaries/partners of WAVES) with a strong record of experimental research on inter-disciplinary and seismology-related topics. WAVES has trained young scientists, working in academia and industry, in how to use this resource effectively, re-introducing the laboratory into the ideas-to-applications pipeline. Experiments helped us to develop new theory, addressing topics of current interest such as acoustic time-reversal, scattering-based imaging, source localisation in seismology and acoustics (including bioacoustics). A truly multidisciplinary network, WAVES has applied these new ideas in a number of contexts: medical elastography has been used as a tool to implement novel analogue models of seismic faults; wave sources were localized by a bio-inspired system making use of very few receivers, etc. Through WAVES, a critical mass of expertise has consolidated, contributing to defining the study of acoustic/elastic wave propagation and wave-based imaging/monitoring as an independent discipline, rich in applications of intellectual and societal relevance.