Abstract: We present the solutions to three important problems in crack propagation and wave scattering in piezoelectric materials. First, an analysis is presented for transient response of a mode-III interfacial crack propagating between two dissimilar piezo-electric half spaces. The dynamic fracture toughness of a piezoelectric interface is examined, which is a central issue related to the interface strength of multi-layered sensors and ferroelectric thin film devices. For mode III crack propagation in piezoelectric materials, an electro-acoustic surface wave, the Bleustein-Gulyaev wave, controls the crack propagation speed. It is shown that the propagation of an interfacial crack, in piezoelectric media may excite an interfacial electro-acoustic surface wave, the Maerfeld-Tournois wave, which is fundamentally different from the mode III interfacial crack propagation in purely elastic media. Moreover, it has been discovered that the existence of the Maerfeld-Tournois wave may play a significant role in determining the dynamic fracture toughness for piezoelectric composites. The second problem solved is the characterization of a Kirchhoff diffraction field in a piezoelectric/ferroelectric material. An exact solution is obtained for the full scattering fields around the tip of a semi-infinite crack, which is electrically conducting and is loaded with both acoustic SH incident waves and plane electrical incident waves. It has been found that a conducting crack in a piezoelectric solid is not completely opaque to the electro-acoustic wave, i.e. the electro-acoustic wave can penetrate and transmit to the other side of the crack surface. Second, the analysis has confirmed that the interaction between the electrical wave and acoustic wave will provide multiple electrical and electro-acoustic head waves. Third, by solving the problem, we have established a rigorous electro-acoustic scattering theory in piezoelectric/ferroelectric media, which is different from the scattering theory in purely elastic media. The characterization of the scattering fields in piezoelectric media provides a unique signature database for electro-acoustic waves in piezoelectric materials. The third problem solved is the diffraction and scattering of plane electro-acoustic incident waves by an interfacial crack between two dissimilar piezoelectric half spaces jointed by a conducting interface. An exact solution is obtained for the full scattering field around the tip of the interfacial crack that is loaded with both acoustic SH incident waves and electric incident waves. (Abstract shortened by UMI.)