Microbial Fuel Cells (MFCs) offer promising prospects in the field of renewable energy since green electrical power is produced by the microbial activity and wastewater is treated simultaneously. MFCs are complex devices whose study requires an interdisciplinary approach as many processes of a diverse nature are involved. Interest in MFC has significantly increased in recent decades, and much scientific effort has been dedicated to making this technology more efficient. However, the focus has been on experimental work, and MFC modeling has tended to be neglected, and only recently has it received more attention with a consequent rise in the number of new MFC models available. Modeling is an,effective tool for gaining a better understanding of MFCs, since it has many advantages in terms of cost and time savings. The present article looks at the state of modeling and simulation of MFCs and outlines and classifies the most prominent models described in the literature. Since modeling approaches can vary greatly from case to case, this work will summarize the advantages and drawbacks of each approach, including not only models based on classic approaches but also those using mathematical optimization techniques. (C) 2015 Elsevier B.V. All rights reserved.