The applicability of artificial neural networks (ANNs) and semi-empirical modelling techniques for correlation and prediction of the filtration characteristics of microfiltration systems was assessed. ANNs were developed to correlate specific cake resistance and steady state flux of dried yeast suspensions in dead-end microfiltration for a range of operating parameters. Trained networks were used in predicting filtration characteristics of previously unseen data, with excellent agreement. Network weights were interpreted for both the specific resistance and flux networks with the effective contribution of each input parameter showing trends that were as expected. A novel neural network technique was developed for the prediction of dynamic flux data in batch stirred microfiltration of bentonite (a clay which forms an aqueous suspension with non-Newtonian rheology), based on eliminating the use of the time series explicitly as an input to the network. This approach reduces the size and complexity of network necessary for correlation and prediction of time series data, thus reducing processing times required, while achieving excellent R2 values for prediction of previously unseen data. This novel approach was also used in the correlation and prediction of batch crossflow microfiltration of bentonite. Drawbacks of the artificial neural network approach include the lack of information obtainable about the physical characteristics of a given system, and the models obtained in this manner are empirical in nature. Although a legitimate approach especially in the modelling of complex systems, the development of physical models to describe these systems is a more fundamental chemical engineering approach to the problem. The use of physical modelling especially in batch systems where the concentration in the system is changing as a function of time is an interesting problem and gives more qualitative insight into what is happening in the system. Semi-empirical models based on the idea of simultaneous particle deposition and cake removal were developed to describe stirred microfiltration, batch crossflow and continuous crossflow of bentonite suspensions. The basic model incorporating a cake removal rate constant k was found to fit qualitatively to stirred filtration data, however the predicted specific cake resistance was over-estimated when compared with experimentally determined values. The basic model was modified by the introduction of two extra terms - a critical flux, J*, below which cake removal by shearing does not take place, and an instantaneous membrane fouling constant, b. The modified model was found to give reasonable approximations to the experimentally determined specific cake resistance for the stirred system, including accurate prediction of the effect of increasing crossflow velocity leading to a decrease in specific cake resistance. Reasonable trends in the model parameters were seen in some but not all cases for the stirred system. On application of this model to batch crossflow filtration data the specific cake resistance was largely overestimated, and this and the model parameters were not found to follow consistent trends. This finding was attributed in part to changing flow regimes in the system due to increases in concentration and crossflow velocity. The modified model incorporating irreversibility was applied to continuous laminar crossflow filtration, and crossflow experiments were extended by flushing of the membrane after filtration to investigate the irreversibility of cake formation in the system. The model was found to fit well to flux decline data, with sensible trends in the specific cake resistance and the model parameters; however, the cake removal by the flushing phase was not well represented by the model.