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 heavily benefit from mathematical modelling. In this paper, the vast literature on hydrodynamic and integrated MBR modelling is critically reviewed. Hydrodynamic models are used at different scales and focus mainly on fouling and only little on system design/optimisation. Integrated models also focus on fouling although the ones including costs are leaning towards optimisation. Trends are discussed, knowledge gaps identified and interesting routes for further research suggested. (C) 2012 Elsevier Ltd. All rights reserved.