In this thesis we report the results of investigations on the rheological response of emulsions to the application of the electric field. A front-tracking finite difference scheme is used in conjunction with Taylor-Melcher leaky dielectric theory to study the problem. The numerical results in different regions of the deformation-circulation map show that the structure formation in regions I and III can be hindered by the hydrodynamic effect. This is opposite to what is observed in the perfect dielectric cases and region II of the map. For perfect dielectric systems, where the electrohydrodynamics effects are absent, droplets form chain-like structures spanning the distance between the electrodes after the application of the electric field. Subsequently, the chains interact with each other to form columns comprising two or more chains. Point-dipole approximation is used to analyze the structure formation and it is shown that it is also applicable to region II where the hydrodynamic effect is weak and the behavior of the system is mainly governed by the dielectrophoretic forces. It is shown that the chain formation is not possible in regions I and III due to the competition between the dipolar force and torque on one side and hydrodynamic effect on the other side. In region I, the hydrodynamic torque prevents the chain formation by competing with the dipolar torque, which tends to align the drops with the electric field. On the other hand, in region III, the repulsive nature of the hydrodynamic effect opposes the attractive dipolar force and does not allow the particles to form stable chains.