This chapter is devoted to the theoretical and numerical study of scattering of electromagnetic waves. We begin with a detailed study of the so-called one-dimensional problem, paying special attention to the link between the problem of propagation in an infinite periodic device and the problem of diffraction by a multilayered structure (Bragg mirror). In addition, we deal with the introduction of a defect in a periodic structure. Scattering by parallel rods is described, through the concept of scattering matrix and the Gamow vectors. We then take up the notion of defect for a two-dimensional crystal and tackle boundary effects in finite-sized crystals. The chapter concludes with some current problems encountered for photonic crystals.