The development of high dielectric constant polymers as active materials in high-performance devices is one of the challenges in polymeric electronics and opto-electronics such as flexible thin-film capacitors, memory devices and microactuators for deformable micromirror technology. A group of poly(vinylidene fluoridetrifluoroethylene) P(VDF-TrFE) based high-dielectric-constant fluoroterpolymers have been developed, which have high room-temperature dielectric constant (K>60) and very high strain level and high energy density. The longitudinal and transverse strain of these materials can reach about -7% and 4.5%, respectively, and the elastic energy density is around 1.1 J/cm^3 under a high electric field of 150 MV/m. The influence on the electromechanical properties of copolymerizing poly(vinylidene fluoride-trifluoroethylene) (PVDF-TrFE) with a third monomer, chlorofluoroethylene (CFE), was investigated. It was found that increasing the CFE content from 0 to 8.5% slowly converts the ferroelectric structure of the copolymer to a relaxor ferroelectric system. This allows for a greatly decreased polarization and dielectric hysteresis and a much higher strain. Above 8.5%, increased CFE content substantially degrades the bulk crystallinity and the Young's modulus. These terpolymers have the potential to achieve above 10 J/cm^3 whole capacity energy density, which makes them good candidates for applications in pulse power capacitors. An all-polymer percolative composite by the combination of conductive polyaniline particles (K>10^5) within a fluoroterpolymer matrix, is introduced which exhibits very high dielectric constant (>7,000). The experimental results show that the dielectric behavior of this new class of percolative composites follows the prediction of the percolation theory and the analysis of the conductive percolation phenomena. The very high dielectric constant of the all-polymer composites which are also very flexible and possess elastic modulus not very much different from that of the insulation polymer matrix makes it possible to induce a high electromechanical response under a much reduced electric field (a strain of 2.65% with an elastic energy density of 0.18 J/cm^3 can be achieved under a low field of 16 MV/m). Data analysis also suggests that in these composites, the non-uniform local field distribution as well as interface effects can significantly enhance the strain responses. Furthermore, the experimental data as well as the data analysis indicate that the conduction loss in these composites will not affect the strain hysteresis. Flexible high dielectric constant electroactive polymers provide potential applications in high-energy-density (HED) energy storage and conversion systems such as lightweight field effect actuators and capacitors.