This book contains the most recent results in the area of strongly inhomogeneous composite structures, including layered materials as well as continua with microstructure. This collection of papers mainly arises from the Euromech Colloquium No. 626 on “Mechanics of High-Contrast Elastic Composites”. Focus is set on the peculiar mechanical behaviour caused by adjoining widely different structural elements (high contrast) in terms of material and/or geometrical properties.