Cellular polymers can be internally charged by "microstorms" (silent or partial discharges) within the voids of the polymer foam. The resulting material, which carries positive and negative charges on the internal void surfaces, is called a ferroelectret. Ferroelectrets behave like typical ferroelectrics, hence they provide a novel class of ferroic materials. The soft foams are strongly piezoelectric and can be used, in a wide range of applications, as transducers for interconverting mechanical and electrical signals. Herein, an overview is provided on the preparation of cellular polymers by physical foaming (extrusion, biaxial stretching, and controlled inflation by pressure treatments), on their charging by "microstorms", on their piezo- and pyroelectricity, and on analogies to ferroelectrics. Finally, a survey of selected applications is presented.