The presented article is an attempt to evaluate the progress in the development of the mathematical simulation of the pressure-driven membrane processes. It was considered more than 170 articles devoted to the simulation of reverse osmosis, nanofiltration, ultrafiltration, and microfiltration and the others published between 2000 and 2010 years. Besides the conventional approaches, which include the irreversible thermodynamics, diffusion and pore flow (and models which consider the membrane surface charge for nanofiltration process), the application of the methods the computational fluid dynamics, artificial neural networks, optimization, and economic analysis have been considered. The main trends in this field have been pointed out, and the areas of using approaches under consideration have been determined. The technological problems which have been solved using the mentioned approaches have also been considered. Although the question of the concentration polarization has not been considered separately, it was defined that, in many cases, the sufficiently accurate model cannot be designed without considering this phenomenon. The findings allow evaluating more thoroughly the development of the simulation of pressure-driven membrane processes. Moreover, the review allows choosing the strategy of the simulation of the considered processes.

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