Hydrogen has been recognized as a promising "fuel" for sustainable power supply in the future. In the hydrogen-based energy systems, electrolyzers and fuel cells, which have similar electrode/electrolyte designs but opposite operational mechanisms, play very important roles in clean hydrogen production from water and electrochemical conversion of hydrogen to electricity, respectively. In the development of the novel technologies, theoretical electrochemical modeling analysis offers an effective and efficient way to study the system characteristics and to optimize the system designs for enhanced performance. The model should take into account the significant cathode/electrolyte/anode overpotentials and mass transport of reactants and products through the nanoporous electrodes. In this study, the theoretical modeling was successfully developed for hydrogen-fed solid oxide fuel cells (SOFC) and hydrogen-producing solid oxide steam electrolyzers (SOSE). Parametric modeling analyses have been performed to develop and optimize the innovative SOFC and SOSE designs, including functionally grade electrodes, reversible SOFC, and proton-conducting SOFC/SOSE. This paper presents the important theoretical modeling features and the detailed parametric modeling results leading to optimal designs of hydrogen SOFC and SOSE.