This chapter aims to sketch the numerical techniques to simulate the photonic band structure of a given periodic dielectric material and illustrates the subtle relations between the basic dielectric structure of photonic crystals and the appearance of photonic bandgaps. It discusses the importance of glass nanospheres for the fabrication of three-dimensional photonic crystals. The chapter deals with a summary and an outlook on current and future developments in the area of nanosphere photonics. It also aims to develop a qualitative and quantitative understanding of light scattering and diffraction by regular arrays of nanospheres. The chapter analyzes the underlying optical principles, which will lead us from the scattering of light by dielectric spheres, over the Bragg diffraction of X-rays by the atoms of a crystal, to the omnidirectional total reflectance of light by photonic nanostructures. It also discusses some numerical examples obtained with MIT Photonic-Bands, an open source program package provided by S. G. Johnson and coworkers.