Dielectric Elastomers (DEs) are an interesting class of active materials that can exhibit coupled electrical and mechanical behaviors, for example they can respond to an external electric field by changing their shape or size. This unique property is known as electrostriction, and makes such materials promising candidates for a wide range of practical applications, and therefore there is a need for the design of DEs with enhanced electromechanical couplings. In this work we investigate the possibility of enhancing the electrostriction by making composites consisting of one or more family of filler phases in a soft dielectric host. We use homogenization techniques to obtain estimates for the effective response of such DECs under general electrical and mechanical loading conditions. Next, we use the homogenization estimates developed in this work to investigate the effect of various microstructural parameters on the overall response of DECs. We also study failure of DECs as characterized by dielectric breakdown and/or the onset of material instabilities. Two types of material instabilities will be considered: Loss of Positive Definiteness (LPD) and Loss of Ellipticity (LE). Finally, we attempt an optimal design for the microstructure of DECs with enhanced electromechanical couplings, which are capable of achieving large electrostrictive strains before the failure. Our results show that composites consisting of a very small concentration of rigid circular fibers with vanishing contrast in the dielectric properties can achieve the largest electrostrictive strains before failure. Finally, we attempt to study DECs in the post-bifurcated deformation regime. This is important since after the composite loses strong ellipticity, the solution of the homogenization problem may bifurcate into a lower energy (with generally softer mechanical response) solution, which is different from the pre-bifurcated solutions. This raises the interesting possibility of operating DECs in their softer post-bifurcated deformation regimes to further increase the maximum achievable electrostrictive strains.