Pervaporation competes with conventional separation techniques, such as distillation and adsorption in organic liquid dehydration, removal or recovery of organic compounds from aqueous solutions, and separation of organic-organic mixtures. Pervaporation is a separation technique relying on the concentration gradient, often expressed as partial vapor pressures, across polymeric or polymer-composite membranes. Those membranes often exhibit a strong trade-off between permeability and selectivity of target compounds, making the search for alternative materials with advanced performance characteristics highly desirable. Metal–organic frameworks (MOFs), a sub-group of porous functionalised materials, have recently demonstrated potential to become a valuable building block in the fabrication of future high-performance pervaporation membranes. MOFs feature unique properties, such as molecular sieve effects, preferential adsorption to the target molecular compounds, and thermal and chemical stability, being suitable for direct applications in pervaporation separation of liquid mixtures. This paper comprehensively examines the current design strategies of MOF-based membranes in pervaporation. The main developments of MOF-based membranes in pervaporation are discussed and the performance of pervaporation processes using MOF-based membranes is also analysed. Furthermore, some perspectives for future development of MOF-based membranes in pervaporation are given.