The dynamics of dielectric rigid particles and liquid drops suspended in another liquid medium and subject to a uniform DC electric field, the study of which forms the field of electrohydrodynamics (EHD), has fascinated scientists for decades. This phenomena is described by the much celebrated Melcher-Taylor leaky dielectric model. The model hypothesises development of interfacial charge on the application of an electric field and prescribes a balance between transient charge, jump in normal Ohmic currents due to finite conductivities of the medium and charge convection arising from interfacial velocity. While there have been numerous studies on the dynamics of particles and drops more conducting than the surrounding liquid medium, weakly conducting particles and drops in strong electric fields, known to undergo symmetry-breaking bifurcations leading to steady rotation known as Quincke electrorotation has received much less attention. Recent experiments have reported a decrease in the effective viscosity of particle under Quincke rotation, thereby providing a means to tune the rheological properties of these suspensions. However, existing models based on an isolated particle, valid for dilute suspension, have been shown to be inaccurate as the density of particles increases. Motivated to resolve these discrepancies, we develop a theoretical model to account for electrohydrodynamic interactions between a pair of spherical particles. We then turn our attention to many particles free to roll on an electrode due to Quincke rotation. Using numerical simulations, we show that electrohydrodynamic interactions between particles give rise to collective motion of these colloidal suspensions. We find emergence of a polar liquid state with large vortical structure in circular confinement. Finally, we address the problem of electrohydrodynamics of deformable liquid drops, first studied by Taylor in 1966. We develop a transient small deformation theory for axisymmetric drops while including the nonlinear charge convection term neglected by previous researchers. We also use numerical simulations based on a novel three-dimensional boundary element method to capture large deformations. These simulations are the first to capture Quincke rotation due to inclusion of the nonlinear charge convection term and show excellent agreement with existing experimental data and theoretical predictions in the small deformation regime.