In this paper the current research and development of electromagnetic metamaterials are reviewed. Firstly, the definition, properties and classification of metamaterials are given. Secondly, commonly used effective medium theories are summarized, including Clausius-Mossoti equation, Maxwell-Garnett equation and its generalization, Bruggemann effective-medium expression, and the Polder-van Santen formula. Then, two retrieval methods for characterising electromagnetic parameters of metamaterials are presented, i.e., the method based on scattering parameters and another based on waveguide measurement. As for possible implementations of metamaterials, six types are demonstrated in the review, namely PCB based metamaterial, graphene based metamaterial, dc metamaterial, transmission-line based metamaterial, metamaterial using dielectric resonators, and anisotropic metamaterials using isotropic layered materials. Moreover, a twodimensional metamaterial, i.e. metasurface, and its working mechanism are also explained. More importantly, several typical applications of metamaterials are illustrated, which are the ultra-thin carpet cloak, microwave gateway, conformal surface plasmon polaritons, digital and programmable metasurface, dc cloak, and graphene based ultra-thin cloak, Luneburg lens, etc. Finally, future development of metamaterials is predicted.

metamaterials  /  metasurface  /  graphene  /  effective medium theory  /  generalized Snell's law