Since the proposition of their concept at the end of the twentieth century, metamaterials have been the subject of many research and discussions in the wave community. More than ten years later the number of related published articles is importantly increasing. On one hand, this success can be attributed to the dream of new physical objects which are the consequences of singular properties of metamaterials. Among them, we can consider the examples of perfect lensing and invisibility cloaking. On other hand, metamaterials also provide new tools for the design of well known wave functions such as antennas for electromagnetic waves. The goal of this book is to propose an overview of the metamaterial concept as a perspective of a new practical tool for wave study and engineering. This includes both the electromagnetic spectrum, from microwave to optics, and the domain of acoustic waves. Discussions on the various topics including in this book have been initiated in the framework of a thematic school proposed by the french network GDR-ONDES in spring 2012.