Facilitated transport membranes for the separation of olefin/paraffin mixtures have long been of interest in separation membrane science because olefins, such as propylene and ethylene, which are important chemicals in petrochemical industries, are currently separated by energy-intensive cryogenic distillation processes. Recently, solid polymer electrolyte membranes containing silver ions have demonstrated remarkable performance in the separation of olefin/paraffin mixtures in the solid state and, thus, they can be considered as alternatives to cryogenic distillation. Here, we review recent progress, and critical issues affecting in the use of facilitated olefin transport membranes; in particular, we provide a general overview with reference to carrier properties, transport mechanisms, and separation performance.