Electrowetting is a versatile tool to reduce the apparent contact angle of partially wetting conductive liquids by several tens of degrees via an externally applied voltage. We studied various fundamental and applied aspects of equilibrium liquid surface morphologies both theoretically and experimentally. Our theoretical analysis showed that surface profiles on homogeneous surfaces display a diverging curvature in the vicinity of the three phase contact line. The asymptotic contact angle at the contact line is equal to Young's angle, independent of the applied voltage. With respect to the morphology of the liquid surface, contact angle variations achieved by electrowetting are equivalent to those achieved by varying the chemical nature of the substrates, except for electric field-induced distortions in a region close to the contact line. Experimentally, we studied the (global) morphology of liquid microstructure substrates with stripe-shaped electrodes. As the local contact angle is reduced by increasing the applied voltage, liquid droplets elongate along the stripe axis as expected. For droplets on a single surface with a stripe electrode, there is a discontinuous morphological transition where elongated droplets transform into translationally invariant cylinder segments with the contact line pinned along the stripe edge and vice versa. If the liquid is confined between two parallel surfaces with parallel stripe electrodes, the elongation of the droplet and its transformation into a translationally invariant morphology with pinned contact lines is continuous. Experimental results are compared to analytical and numerical models.