► Individual MBR biokinetics and filtration models were critically reviewed. ► Modelling studies mainly focused on knowledge development. ► More process model validation is required, including experimental data collection. ► Future modelling studies should focus on model application, preferably at full scale. ► Future modelling studies should make use of good modelling practice. Membrane bioreactor technology exists for a couple of decades, but has not yet overwhelmed the market due to some serious drawbacks of which operational cost due to fouling is the major contributor. Knowledge buildup and optimisation for such complex systems can significantly benefit from mathematical modelling. In this paper, the vast literature on modelling MBR biokinetics and filtration is critically reviewed. It was found that models cover the wide range of empirical to detailed mechanistic descriptions and have mainly been used for knowledge development and to a lesser extent for system optimisation/control. Moreover, studies are still predominantly performed at lab or pilot scale. Trends are discussed, knowledge gaps identified and interesting routes for further research suggested.