Liquid membranes have traditionally been employed for liquid/liquid mass transfer and have found applications in industrial, biomedical and analytical fields as well as in hydrometallurgical processes, wastewater treatment and remediation of polluted groundwater. However, in spite of the known advantages of liquid membranes, there are few examples of industrial application. The development of reliable mathematical models and design parameters (mass transport coefficients and equilibrium or kinetic parameters associated with the interfacial reactions) is a necessary step for design, cost estimation, process optimisation and scale-up. This work reports an overview of the different approaches that have been proposed in the literature to the mathematical modelling of liquid membrane separation processes in hollow fibre contactors providing, at the same time, a useful guideline to characterise the mass transport phenomena and a tool for the optimal design and intensification of separation processes. (C) 2009 Society of Chemical Industry