  The insulating state of matter is characterized by the excitation spectrum,
but also by qualitative features of the electronic ground state. The insulating
ground wavefunction in fact: (i) displays vanishing dc conductivity; (ii)
sustains macroscopic polarization; and (iii) is localized. The idea that the
insulating state of matter is a consequence of electron localization was first
proposed in 1964 by W. Kohn. I discuss here a novel definition of electron
localization, rather different from Kohn's, and deeply rooted in the modern
theory of polarization. In fact the present approach links the two features
(ii) and (iii) above, by means of essentially the same formalism. In the
special case of an uncorrelated crystalline solid, the localization of the
many-body insulating wavefunction is measured - according to our definition -
by the spread of the Wannier orbitals; this spread diverges in the metallic
limit. In the correlated case, the novel approach to localization is
demonstrated by means of a two-band Hubbard model in one dimension, undergoing
a transition from band insulator to Mott insulator.
