Processing of colloidal gels with electrified interfaces to form ceramic bulk and composite materials as well as coatings of complex shapes with well definded structures in the nanoscale requires the understanding of fundamental role of the coupling between hydrodynamic and electric interactions in colloidal deposition and colloidal arrangement. In this article, fundamental equations of electrohydrodynamics of membrane supported electrophoretic deposition (EPD) as well as exemplary numerical FEM-simulations of electrophoretically deposited colloidal gels are presented. Based on microfluidic physics a model is then used to study electrohydrodynamic EPD phenomena, especially electroosmotic flow incorporated with modulated surface potentials, particle interactions and electrostatic potentials. Some practical applications of EPD as well as visions of general purpose of the computational modelling results were given.