Metamaterials are engineered composites. Much of the effort in the electrical engineering, material science, physics, and optics communities emphasized constructing efficient metamaterials and using them for potentially novel applications in antenna and radar design, subwavelength imaging, and invisibility cloak design. The purpose of this chapter is to provide a detailed introduction to the basic metamaterial modelling approaches and an overview of innovative phenomena enabled by metamaterials. While high tunability of the electromagnetic properties might be provided by metamaterial structures and metasurfaces, the former option has not yet been used to solve this problem. By means of the freedom of design provided by metamaterials, we propose the ways to redirect electromagnetic fields and demonstrate a design strategy.