Abstract: This article summarizes the new development of small-amplitude motionssuperposed on finite biasing or initial fields in an electroelastic body,which is called the biasing field method.It begins with a summary of the nonlinear theory of electroelasticity,as the theoretical foundation for the theory of small displacement fields superposed on abias. The development of the theory for small displacement fieldssuperposed on a bias, and the development ofstructural theories for electroelastic beams, plates and shells underbiasing fields are discussed. Applications of the theory for small displacement fieldssuperposed on biasing fields in the buckling of thin electroelasticstructures, frequency stability of piezoelectric resonators for time-keepingand telecommunication, acoustic wave sensors based on frequency shifts dueto biasing fields, characterization of nonlinear electroelastic materials bypropagation of small-amplitude waves in electroelastic bodies under biasingfields, and electrostrictive ceramics under a biasing electricfield are reviewed. A summary of some current and possible future researchtopics in this field is given. The article contains 166 references.