AbstractIn the challenge to increase photosynthetic rate per leaf area mathematical models of photosynthesis can be used to help interpret gas exchange measurements made under different environmental conditions and predict underlying photosynthetic biochemistry. To do this successfully it is important to improve the modelling of temperature dependencies of CO2 assimilation and gain better understanding of internal CO2 diffusion limitations. Despite these shortcomings steady‐state models of photosynthesis provide simple easy to use tools for thought experiments to explore photosynthetic pathway changes such as redirecting photorespiratory CO2, inserting bicarbonate pumps into C3 chloroplasts or inserting C4 photosynthesis into rice. Here a number of models derived from the C3 model by Farquhar, von Caemmerer and Berry are discussed and compared.