We review numerical methods developed by the authors for the study of both static and dynamic electrowetting problems. For the study of static problems that can be written in terms of minimization of an energy, a boundary integral method for the computation of charge density distributions is developed. We illustrate its use with the computation of static shapes of charged drops over a flat surface and under the influence of an external potential. For the study of dynamic problems, where drops can move over a solid substrate we develop a phase-field model. Such models replace the sharp interfaces between two fluids by a so-called diffuse interface. We illustrate the use of the phase-field model with the calculation of drops spreading and moving in an electrowetting system. (C) Koninklijke Brill NV, Leiden, 2011