By way of prerequisites, we recall a few mathematical features of surface wave propagation in Section II and the notion of resonance coupling between modes in Section III. The exemplary case of Bleustein-Gulyaev waves in linear piezoelectrics is then briefly examined in Section IV. SH surface waves in inhomogeneous isotropic linear elasticity are the subject of Section V. Surface modes with SH elastic polarization in elastic ferroelectrics and elastic ferromagnets are examined in Sections VI and VII, respectively. Most of the models and methods reported rely heavily on the advances made in rational continuum mechanics during the last 15 years, especially insofar as nonlinear theories with finite strains provide the starting point in several cases and systematic use of the method of superimposition of small dynamical signals on finite bias static fields and the anisotropy inducement by these bias fields are considered.