  Piezoelectrics have long been studied using parameterized models fit to
experimental data, starting with the work of Devonshire in 1954. Much has been
learned using such approaches, but they can also miss major phenomena if the
materials properties are not well under-stood, as is exemplified by the
realization that low-symmetry monoclinic phases are common around morphotropic
phase boundaries, which was missed completed by low-order Devonshire models,
and can only appear in higher order models. In the last 15 years, a new
approach has developed using first-principles computations, based on
fundamental physics, with no essential experimental input other than the
desired chemistry (nuclear charges). First-principles theory laid the framework
for a basic understanding of the origins of ferroelectric behavior and
piezoelectric properties. The range of properties accessible to theory
continues to expand as does the accuracy of the predictions. We are moving
towards the ability to design materials of desired properties computationally.
Here some of the fundamental developments of our understanding of piezoelectric
material behavior and ability to predict a wide range of properties using
theoretical methods are reviewed.
