Electric polarization is one of the basic quantities in physics, essential to the theory of dielectrics, effective charges in lattice dynamics, piezoelectricity, ferroelectricity, and other phenomena. However, descriptions in widely used texts are often based upon oversimplified models that are misleading or incorrect. The basic problem is that the expression for a dipole moment is ill defined in an extended system, and there is no unique way to find the moment as a sum of dipoles by “cutting” the charge density into finite regions. For extended matter such as crystals, a theory of polarization formulated directly in terms of the quantum mechanical wavefunction of the electrons has only recently been derived, with an elegant formulation in terms of a Berry's phase and alternative expressions using Wannier functions. The other essential property of insulators is “localization” of the electrons. Although the concept of localization is well known, recent theoretical advances have provided new quantitative approaches and demonstrated that localization is directly measurable by optical experiments. This chapter is closely related to Ch. 21 on Wannier functions, in particular to the gauge-invariant center of mass and contribution to the spread of Wannier functions ΩI of Sec. 21.3.