  The dipole moment of any finite and neutral system, having a
square-integrable wavefunction, is a well defined quantity. The same quantity
is ill-defined for an extended system, whose wavefunction invariably obeys
periodic (Born-von Karman) boundary conditions. Despite this fact, macroscopic
polarization is a theoretically accessible quantity, for either uncorrelated or
correlated many-electron systems: in both cases, polarization is a rather
"exotic" observable. For an uncorrelated-either Hartree-Fock or
Kohn-Sham-crystalline solid, polarization has been expressed and computed as a
Berry phase of the Bloch orbitals (since 1993). The case of a correlated and/or
disordered system received a definitive solution only very recently (1998):
this latest development allows us present here the whole theory from a novel,
and very general, viewpoint. The modern theory of polarization is even relevant
to the foundations of density functional theory in extended systems.
