Wastewater treatment processes with granular sludge are compact and are becoming increasingly popular. Interest has been accompanied by the development of mathematical models. This contribution simultaneously reviews available models in the scientific literature for anaerobic, aerobic and partial nitritation-anammox granular sludge reactors because they comprise common phenomena (e.g. liquid, gas and granule transport) and thus pose similar challenges. Many of the publications were found to have no clearly defined goal. The importance of a goal is stressed because it determines the appropriate model complexity and helps other potential users to find a suitable model in the vast amount of literature. Secondly, a wide variety was found in the model features. This review explains the chosen modelling assumptions based on the different reactor types and goals wherever possible, but some assumptions appeared to be habitual within fields of research, without clear reason. We therefore suggest further research to more clearly define the range of operational conditions and goals for which certain simplifying assumptions can be made, e.g. when intragranule solute transport can be lumped in apparent kinetics and when biofilm models are needed, which explicitly calculate substrate concentration gradients inside granules. Furthermore, research is needed to better mechanistically understand detachment, removal of influent particulate matter and changes in the mixing behaviour inside anaerobic systems, before these phenomena can be adequately incorporated in models. Finally, it is suggested to perform full-scale model validation studies for aerobic and anammox reactors. A spreadsheet in the supplementary information provides an overview of the features in the 167 reviewed models.