This work provides an alternative perspective on mechanical and electromagnetic waves in structured materials. Experts from both fields present up-to-date developments in theory and applications, and emphasize fundamental concepts, which unify wave science. The book is pitched at a level suitable for research students and those coming from other fields, who wish to learn about topics at the forefront of research into control and properties of waves in structured media. Particular areas discussed in depth include materials exhibiting band gaps for optical and mechanical waves, localization and homogenization, composite materials, and fundamental wave properties such as group and energy velocities in the presence of strong scattering. The papers in this book arise from a Symposium held at the University of Sydney in January 1999.