The thermal growth of oxide film on top of a metal surface can be viewed as an electrochemical process and unless at very thin-film stage, the growth kinetics is largely controlled by mass transport (ionic) across the oxide layer. The latter process is also essential to solid oxide fuel cells (SOFCs). Differences are that for the former, the ionic transport is the slower the better for the sake of oxidation resistance, while for the latter, the faster the better in terms of cell performance. From the modeling perspective, both the processes involve a concern regarding the characteristic length scale that is the Debye length. We present an electrochemical phase-field model for thermal oxidation together with a multi-scale scheme which continuously models oxide film growth across orders of magnitude in length around the Debye length. On the other hand, phase-field modeling regarding SOFCs is approached at two length scales at and above the Debye-length scale. Issues in oxidation modeling especially the coupled-currents condition and local equilibrium, and their counterparts in SOFC modeling will be discussed.