Photonic crystals, periodic arrangements of two or more dielectric materials, have been studied for more than two decades as a means of controlling and manipulating the flow of light. These lectures describe recent progress in designing non-periodic photonic solids. The aim is to find arrangements of dielectric materials that produce substantial complete photonic band gaps that block light in all directions and for all polarizations over a range of frequencies. Methods are described for constructing quasicrystalline examples with a wide range of rotational symmetries and a special class of isotropic, disordered photonic band gap materials.