Optics with applications to photonics is a key enabling technology in telecommunications and optical computing. In the last decade, the technology to fabricate structures on optical to sub-optical wavelength-scale has matured and opened the way for the development of a new generation of photonics devices, which once inserted in the applications is expected to increase systems performace significantly. Recent years have witnessed an exponential growth in this field. This book presents the role that nonlinear optics plays in these new artificial materials and structures, supported by an adequate development of theoretical and numerical methods to study new geometries.