This is a review article on the mechanics of small-amplitude motions superposed on finite biasing or initial fields in an electroelastic body. It begins with a summary of the nonlinear theory of electroelasticity, which is the theoretical foundation for the theory of small fields superposed on a bias. This theory, obtained by different approaches, and the development of structural theories for electroelastic beams, plates, and shells under biasing fields are discussed. Applications of these theories for small fields superposed on biasing fields in the buckling of thin electroelastic structures, frequency stability of piezoelectric resonators for time-keeping and telecommunication, acoustic wave sensors based on frequency shifts due to biasing fields, characterization of nonlinear electroelastic materials by propagation of small-amplitude waves in electroelastic bodies under biasing fields, and electrostrictive ceramics which operate under a biasing electric field are reviewed. A summary of some current and possible future research topics in this field is given. The article contains 166 references.