The present book is focused on the study of unprecedented control and manipulation of light by photonic crystals (PCs) and their applications. These are micro- or usually nano-structures composed of periodic indexes of refraction of dielectrics with high refractive index contrast. They exhibit optical frequency band gaps in analogy to electronic bands for a periodic potential of a semiconductor crystal lattice. The gemstone opal and butterflys feathers colours are already referred to as natural examples of photonic crystals. The characteristics of such supper-lattices were first reported by Yablonovitch in 1987. The exploitation of photonic crystals is a promising tool in communication, sensors, optical computing, and nanophotonics. Discussed are the various features of one-dimensional (1D) and two-dimensional (2D) photonic crystals, photonic quasi crystals, heterostuctures and PC fibres under a variety of conditions using several materials, and metamaterials. It also focuses on the applications of PCs in optical computing.