Epithelial membrane transporter kinetics portray an irrefutable role in solute transport in and out of cells. Mechanistic models are used to investigate the transport of solutes at the organ, tissue, cell or membrane scale. Here, we review the recent advancements in using computational models to investigate epithelial transport kinetics on the cell membrane. Various methods have been employed to develop transport phenomena models of solute flux across the epithelial cell membrane. Interestingly, we noted that many models used lumped parameters, such as the Michaelis-Menten kinetics, to simplify the transporter-mediated reaction term. Unfortunately, this assumption neglects transporter numbers or the fact that transport across the membrane may be affected by external cues. In contrast, more recent mechanistic transporter kinetics models account for the transporter number. By creating models closer to reality researchers can investigate the downstream effects of physical or chemical disturbances on the system. Evidently, there is a need to increase the complexity of mechanistic models investigating the solute flux across a membrane to gain more knowledge of transporter-solute interactions by assigning individual parameter values to the transporter kinetics and capturing their dependence on each other. This change results in better pharmacokinetic predictions in larger scale platforms. More reliable and efficient model predictions can be made by creating mechanistic computational models coupled with dedicated in vitro experiments. It is also vital to foster collaborative efforts among transporter kinetics researchers in the modeling, material science and biological fields.