We present a diffuse interface model for the phenomenon of electrowetting on dielectric and present an analysis of the arising system of equations. Moreover, we study discretization techniques for the problem. The model takes into account different material parameters in each phase and incorporates the most important physical processes, such as incompressibility,electrostatics and dynamic contact lines; all necessary to model the real phenomena. The arising nonlinear system couples the variable density incompressible Navier-Stokes equations for velocity and pressure with a Cahn-Hilliard type equation for the phase variable and chemical potential, a convection diffusion equation for the electric charges and a Poisson equation for the electric potential. Numerical experiments are presented, which show splitting/coalescence of droplets and contact line pinning. This presentation is based on joint work with A. Salgado (U. of Tennessee) and R. Nochetto (U. of Maryland).