The research conducted in the context of this PhD, lies on the cross section between multi-scale modeling of flow in porous media, electrochemical diffusion and reaction, in combination with Shape and Structural Optimization techniques. More specifi-cally, we have followed two lines of action for dealing with this problem. On the one hand, we attempt to perform optimization of a Solid Oxide Fuel Cell in the macro scale. Focusing on the anode interconnect, we wish to come up with an optimum interconnect design. This can be achieved in principal, since the interconnect needs to satisfy two major requirements. On the one hand, it needs to secure the intake of fuel into the cell, fact that would require an as low hydraulic resistance as possible, i.e. ideally an open channel and on the other hand to exhibit an as high as possible electronic conductance, which in the ideal case would mean an area blocked completely by a material with high conductivity such as coated stainless steel. The balance between these two competing, oppositely driving forces, indicate that there should be a design that satisfies in the best way both. Similar problems have been successfully dealt by structural-topology optimization approaches and this is one of the first attempts to apply this combination of set of tools to fuel cells. Describing in a nutshell the methodology followed, we use Comsol's ability to create Matlab scripts which incorporate the desired physics of the problem (Partial Differential Equations, treating the setup as continuum) and we combine these scripts with the ones containing the optimization routines like the Method of Moving Asymptotes (MMA). Success in obtaining such a design, would greatly affect the overall cell's efficiency rendering the Solid Oxide Fuel Cell more competitive in the sustainable energy basket of solutions. In this project, consulting role was also undertaken by researchers at National Center for Sustainable Energy, Risø and more specifically by Dr. Martin Søgaard, Dr. Henrik Frandsen and Dr. Peter Vang Hendriksen (team leader). The other approach is based on attacking the problem in the micro-scale. Taking as starting point the homogenization method for getting an upscaled equation for the diffusion of ion vacancies in a fuel cell's cathode, we derive formulas that express the Area Specific Resistance (ASR) of the electrode as a function of geometric parameters, such as the tortuosity and the porosity of the material, for preselected micro-structures. Furthermore, we apply optimization techniques to lead this ASR to minimization. This work has been the fruit of collaboration with Professor Sossina Haile at the California Institute of Technology (Caltech) and with assistant Professor Francesco Ciucci at the Hong Kong University of Science and Technology (HKUST). As a complementary in this modeling work, we have also developed other activities, leading to either already accepted, submitted or soon to be submitted publications. These additional to the main focus directions, have had three components. In chronological terms, first was the experimental contribution to the calculation of the optimum percentage of Zirconium in Zirconium Doped Ceria (ZDC) in the context of my external stay at the California Institute of Technology. Secondly, we have also participated in testing the compound of magnesium hydrides encapsulated in PMMA for a set of experiments aiming at the development of a mass production method through laser ablation for cheap and effective hydrogen storage. This work was done in collaboration with Dr. Athanasios Stubos at the National Center for Scientific Research, in Athens, Hellas. Towards the end of the PhD, we have also worked close with Professor Ciucci once more, on assessing the identifiability of the physical parameters, surface reaction rate k and bulk diffusion coefficient D, as functions of the Biot number and the normalized by the diffusional time scale annealing time, in Isotope Exchange Depth Profiling Measurements (IEDP). Besides computing the expected relative errors, we have also proposed a novel approximation for the confidence intervals on k and D.