Solid oxide fuel cells (SOFCs) have been attracting considerable attention as prospective power sources with a variety of applications. Much current research is directed towards lowering the SOFC operating temperature in order to reduce the costs related to insulation, materials, start-up and degradation. Development of versatile technologies is required to fabricate a SOFC with a thin-film electrolyte membrane to decrease ohmic losses at reduced temperatures and to form graded electrodes that have superior electrochemical performance. Electrophoretic deposition (EPD) is one of the most technologically flexible and cost-effective methods currently available for the thin film formation. This review briefly highlights the fundamental regularities and mechanisms of EPD and shows the evolution of the mathematical model of EPD considering classical and recent studies in this area. It presents current approaches to overcoming the challenges in the realization of the EPD process such as the choice of dispersion medium and additives, preparation of stable suspensions, bubble-free deposition from aqueous suspensions, formation of substrates with optimized porosity and conductivity and deposition on non-conducting substrates. It also summarizes the latest advances in deposition of different SOFCs’ functional layers (dense, porous and multilayered) and entire cell structures, including micro-tubular cells.