ABSTRACT We review theoretical results on anti-plane motions of polarized ceramics based on the linear theory of piezoelectricity. Solutions to dynamic problems of the propagation of bulk acoustic waves (BAW) and surface acoustic waves (SAW), vibrations of finite bodies, and applications to various piezoelectric devices including piezoelectric waveguides, resonators, mass sensors, uid sensors, actuators, nondestructive evaluation, power harvesters (generators), transformers, and power transmission through an elastic wall by acoustic waves are discussed. Complications due to material inhomogeneity, initial stress, electromagnetic coupling, electric field gradient and semiconduction are also discussed. The paper cites 82 references.