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The article presents a comparison of mathematical models of steam methane reforming. The analysis is divided into two parts. The first concerns the reforming process using separate steam reformers. The second part of the article compares models of steam methane reforming processes directly inside fuel cells. Due to the fact that the steam reforming process takes place at very high temperatures, internal steam reforming can only be carried out in high temperature fuel cells. Therefore, the second part of the article deals with molten carbonate fuel cells and solid oxide fuel cells powered by methane. In the case of both of fuel cells, the methane steam reforming may take place directly on the anodes of these electrochemical devices. The mathematical models (for both external and internal reforming) were compared based on available experimental data. In this analysis of mathematical models, particular attention was paid to the causes of discrepancies between the mathematical models and the experimental data. The steam reforming process is influenced by a number of different parameters such as: temperature, ratio of the amount of water vapor to carbon contained in the fuel (steam to carbon ratio), reaction time, presence of a catalyst, type of catalyst and many others. The models presented in this article were also compared in terms of taking into account various parameters that may affect the process of steam reforming. An attempt was also made to assess the accuracy of mathematical models. Unfortunately, for most of the equations considered in this article, numerical values for inaccuracies are not given or described as acceptable or minor. • Review of mathematical models of SMR. • The kinetics models of the steam methane reforming reaction. • Description of mathematical models for the molten carbonate fuel cell (MCFC). [ABSTRACT FROM AUTHOR]