Electrowetting is a commonly used tool to manipulate sessile drops on hydrophobic surfaces. By applying an external voltage over a liquid and a dielectric-coated surface, one achieves a reduction of the macroscopic contact angles for increasing voltage. The electrostatic forces all play out near the contact line, on a scale of the order of the thickness of the solid dielectric layer. Here we explore the case where the dielectric is a soft elastic layer, which deforms elastically under the effect of electrostatic and capillary forces. The wetting behaviour is quantified by measurements of the static and dynamic contact angles, complemented by confocal microscopy to reveal the elastic deformations. Even though the mechanics near the contact line is highly intricate, the macroscopic contact angles can be understood from global conservation laws in the spirit of Young-Lippmann. The key finding is that, while elasticity has no effect on the static electrowetting angle, the substrate's viscoelasticity completely dictates the spreading dynamics of electrowetting.