The membrane-based liquid desiccant air dehumidification method had been reviewed based on the momentum, thermal, and mass transports, the performance analysis, and the thermodynamics. The parallel-plate membrane dehumidifiers (PMC) and hollow fiber membrane dehumidifiers (HFMC) with the cross-flow, quasi-counter flow, and counter flow configurations were summarized. The adiabatic and internally-cooled membrane dehumidifiers were described. The single-stage and the multistage membrane-based liquid desiccant air dehumidification (M-LDAD) systems to enhance their performances were analyzed. The internally-cooled quasi-counter flow PMC of the side in and side out type and hexagonal type were the promising alternatives. The counter flow and cross-flow HFMC were suitable for the small and relatively large air flow rates, respectively. The inclined flow type should be avoided to prevent from the performance deterioration. The internally-cooled HFMC with the cooling coils inside the solution channels between the neighboring short sub-contactors might have better performances with at the expenses of increasing equipment and operating costs. Effects of the membrane deformations on the momentum, thermal, and mass transports both in the PMC and HFMC should be studied. The randomly distributions of the hollow fiber tubes should be avoided. The multistage M-LDAD systems based on the internally-cooled PMC and HFMC complementarily driven by the waste energy and renewable energy sources were the better choices in the practical application whose thermodynamic and dynamics should be investigated. (C) 2019 Elsevier Ltd. All rights reserved.