  This article reviews the polarizability model and its applications to
ferroelectric perovskite oxides. The motivation for the introduction of the
model is discussed and nonlinear oxygen ion polarizability effects and their
lattice dynamical implementation outlined. While a large part of this work is
dedicated to results obtained within the self-consistent-phonon approximation
(SPA), also nonlinear solutions of the model are handled which are of interest
to the physics of relaxor ferroelectrics, domain wall motions, incommensurate
phase transitions. The main emphasis is to compare the results of the model
with experimental data and to predict novel phenomena.
