T he idea of a new class of media that has unusual properties with respect to electromagnetic wave propagation is generally attributed to the Russian physicist Victor Veselago [1]. He considered what would be the consequences if one could create or find materials for which the dielectric permittivity ε and the magnetic permeability µ were both negative. He deduced that one striking outcome would be that the refractive index of the material would seem to be negative, causing the incident and refracted waves to lie on the same side of the normal to the interface between a 'standard' medium and the new medium. This phenomenon is now known as negative refraction (Figure 1(a)) and is associated with other phenomena in which the sign of the refractive index is reversed, such as Doppler shift, Cherenkov angle, Goos-Hänchen shift and radiation pressure. Another consequence of a negative refractive index is that the electric, magnetic and wave vectors form a left-handed triad, rather than the right-handed triad found in dielectrics. For this reason, such materials are called left-handed media, or sometimes double-negative media.If one considers the conservation of momentum at the interface between a standard material and a left-handed metamaterial in which negative refraction is occurring (Figure 1(b)), two viewpoints are valuable. In the first, the metamaterial is regarded as a continuous medium characterized by an optical refractive index (or perhaps a permittivity tensor), and thus conservation of momentum requires the index to be negative. In the second, the metamaterial is regarded as being composed of discrete elements (perhaps at the level of atoms or molecules, or larger) separated by a vacuum. This means that left-handed metamaterials must have an internal structure whose strong interaction provides momentum transfer parallel to the interface, and also in the correct direction, much as a diffraction grating or crystal can. Hence, we require a well-designed structured material to provide this new behavior, and it should be structured on a scale much finer than the wavelength of incident light if it is to be regarded as a new type of solid, rather than just a diffraction grating or stack of diffraction gratings.Related fields of science already exist in which structured materials are used to give desired optical properties. One of these is the study of composite materials, for which the most authoritative account may be found in a book by Milton [2]. This field dates back to Egyptian and Roman times, when different colors were given to glass by mixing chosen metallic particles into the glass matrix. Optical composite materials are generally used in the quasistatic limit, where the particle size is much finer than the wavelength of incident light. One can use electrostatics to calculate an effective dielectric permittivity or refractive index for the particle-matrix structure, and exploit the effective permittivity or We discuss the topics of metamaterials-electromagnetic composites offering simultaneous control of...