The solid oxide fuel cell (SOFC) is one of the most promising fuel cells for direct conversion of chemical energy to electrical energy with the possibility of its use in co-generation systems because of the high temperature waste heat. Various mathematical models have been developed for three geometric configurations (tubular, planar, and monolithic) to solve transport equations coupled with electrochemical processes to describe the reaction kinetics including internal reforming chemistry in SOFCs. In recent years, considerable progress has been made in modeling to improve the design and performance of this type of fuel cells. The numbers of the contributions on this important type of fuels have been increasing rapidly. The objective of this paper is to summarize the present status of the SOFC modeling efforts so that unresolved problems can be identified by the researchers. (c) 2006 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved.