This paper reviewed the mass-transfer of the target substance in the biofilm-covered granular activated carbon (BGAC) system. Representative hypotheses and equations related to developing the mathematical models for a BGAC reactor were discussed in terms of granular activated carbon (GAC) phase, biofilm phase and bulk solution, respectively. It should be noted that discrete phenomena such as biofilm detachment due to erosion or sloughing were not considered for the modeling system. Recent advances on this topic were thoroughly updated, as well as those models proposed in past decades. It appears that a general BGAC model has not been available so far, and further efforts are required to obtain models more approaching of the physical mechanism of this complicate system. Copyright (c) 2012 Society of Chemical Industry