**Abstract**

Anaerobic granule sludge is a self-forming biofilm. This biofilm can be developed without the presence of bio-carriers. Anaerobic granule sludge-based technologies are dominant technologies in the field of anaerobic wastewater treatment. Although they are successful technologies, many efforts are still needed for a better understanding of the granules and granule-based reactors because reactor failure can occur. Here, reactor modeling is highly helpful in understanding the performance of anaerobic bioreactors. A model that can accurately model bioprocesses in a sludge bed reactor and predict concentrations of effluent components is valuable. This is because the model can provide insights into the reactor and be useful in reactor control. Current models of granules are models on bioprocesses in a single granule sludge or on the hydrodynamics and biokinetics in a sludge bed reactor. Here, we review advances in reactor model and its applications as well as limitations and further improvements in the models.

**Keywords:** anaerobic, granule, model, wastewater, sludge, modeling
