The aim of this chapter is to review the state of the art of the possibilities and existing knowledge on characterization of mechanical and coupling properties and damage detection in piezoelectric ceramics. To address the theoretical problem with a proper rational basis, a review of numerical and experimental techniques to solve the so-called inverse problem of characterization of properties and damage is given. Finally, the relevant details of finite element and boundary element formulations and implementation when addressing correct damage simulation in piezoelectric ceramics (Perez-Aparicio et al. (2007)) is presented. In recent years, the theoretical framework of inverse problems has been developed to understand and formalize the property and damage characterization problems. This theory has been applied in a variety of continuum mechanics applications, by the groups of Liu & Chen (1996), Oh et al. (2005), Pagano (1970), Rus et al. (2005) and Tarantola & Valette (1982). There is a growing body of knowledge in identification inverse problems for elasticity, like the groups of Tardieu & Constantinescu (2000) or Bonnet & Constantinescu (2005), but due to the intrinsic coupling of magnitudes, the formulation of the piezoelectric problems is more complex than in elastic problems. Despite this difficulty, the electric field and its coupling with the elastic field has the potential to be exploited in monitoring piezoelectrics and in the solution of the inverse problem. Inverse problem techniques have been applied specifically for the piezoelectric ceramics for: