This is a review article on a few special topics in piezoelectricity: gradient and nonlocal theories, fully dynamic theory with Maxwell equations, piezoelectric semiconductors, and motions of rotating piezoelectric bodies. They all require some extension of the classical theory of piezoelectricity. They are relatively new, more advanced, and growing subjects with applications or potential applications in various electromechanical devices. The article contains 209 references. (In memory of Raymond D. Mindlin (1906–1987)).