Abstract
This review presents the developments in the mathematical models for various bioelectrochemical systems. A number of modeling approaches starting with the simple description of biological and electrochemical processes in terms of ordinary differential equations to very detailed 2D and 3D models that study the spatial distribution of substrates and biomass, have been developed to study BES performance. Additionally, mathematical models focused on studying a particular process such as ion diffusion through membrane and new modeling approaches such as artifcial intelligence methods, cellular network models, etc., have also been described. While most mathematical models are still focused on performance studies and optimization of microbial fuel cells, new models to study other BESs such as microbial electrolysis cell, microbial electrosynthesis and microbial desalination cell have also been reported and discussed in this review.