Air dehumidification is of vital importance in building air conditioning and production safety. Semipermeable membrane module is a novel heat and mass exchanger, which separates the air and liquid desiccant to overcome desiccant droplet carry-over problem in traditional direct-contact systems. Recently, some research works have been carried out in mathematical modelling and experimental testing of membrane-based liquid desiccant dehumidification technology. Compared with the experimental testing, the mathematical modelling has advantages of significant time and cost reductions, practically unlimited level of detail, more profound understanding of physical mechanism and better investigation of critical situation without any risks. This paper presents a comprehensive review of various modelling methods for two types of membrane-based liquid desiccant modules: fiat plate and hollow fiber. (C) 2018 Elsevier Ltd. All rights reserved.