Recent advances in computational techniques have allowed the application of computational tools to study heterogeneous functional materials (HeteroFoaMs) in the solid oxide fuel cell (SOFC) from the quantum (sub-atomic) to atomistic to the continuum scales. However, knowledge gained from a particular computational technique can only provide insight at that specific scale. There has been a recent interest to develop a more cohesive effort so that results obtained from models across a particular spatial dimension can be used to extract additional insight across a larger range of length scales. This review article surveys recent progress in the modeling and simulation of SOFCs, and relates them to the relevant physical phenomena and length/time scales. We then proceed to review the various numerical techniques used, and their applicability across the length and time scales. (C) 2011 Elsevier BV. All rights reserved.