In this paper, the transport phenomena in four common membrane distillation (MD) configurations and three popular modelling approaches are introduced. The mechanism of heat transfer on the feed side of all configurations are the same but are distinctive from each other from the membrane interface to the bulk permeate in each configuration. Based on the features of MD configurations, the mechanisms of mass and heat transfers for four configurations are reviewed together from the bulk feed to the membrane interface on the permeate but reviewed separately from the interface to the bulk permeate. Since the temperature polarisation coefficient cannot be used to quantify the driving force polarisation in Sweeping Gas MD and Vacuum MD, the rate of driving force polarisation is proposed in this paper. The three popular modelling approaches introduced are modelling by conventional methods, computational fluid dynamics (CFD) and response surface methodology (RSM), which are based on classic transport mechanism, computer science and mathematical statistics, respectively. The default assumptions, area for applications, advantages and disadvantages of those modelling approaches are summarised. Assessment and comparison were also conducted based on the review. Since there are only a couple of full-scale plants operating worldwide, the modelling of operational cost of MD was only briefly reviewed. Gaps and future studies were also proposed based on the current research trends, such as the emergence of new membranes, which possess the characteristics of selectivity, anti-wetting, multilayer and incorporation of inorganic particles.