Materials that have periodic microstructure on a given length scale display a strong modification of electromagnetic density of states for radiation wavelength at the corresponding scale. These structures are known as photonic crystals. Under certain circumstances the density of states vanishes completely for a range of wavelengths, and the material is said to have a photonic band gap, whereby optical propagation is completely suppressed. This affords the possibility of optical control useful for a range of applications including novel filters, waveguides, and efficient laser structures. In this paper, a range of fabrication methods of these crystals is described, together with basic theory and some properties and applications. Particular attention is given to two-dimensionally periodic materials in the form of optical fibre (the photonic crystal fibre and photonic band gap fibre), which have the potential for high-power optical guidance. Three-dimensionally periodic materials designed to control microwave radiation are also described.