Gas separation for industrial, energy, and environmental applications requires low energy consumption and small footprint technology to minimize operating and capital costs for the processing of large volumes of gases. Among the separation methods currently being used, like distillation, amine scrubbing, and pressure and temperature swing adsorption, membrane-based gas separation has the potential to meet these demands. The key component, the membrane, must then be engineered to allow for high gas flux, high selectivity, and chemical and mechanical stability at the operating conditions of feed composition, pressure, and temperature. Among the new type of membranes studied that show promising results are the inorganic-based and the metal-organic framework-based mixed-matrix membranes (MOF-MMMs). A MOF is a unique material that offers the possibility of tuning the porosity of a membrane by introducing diffusional channels and forming a compatible interface with the polymer. This review details the origins of these membranes and their evolution since the first inorganic/polymer and MOF/polymer MMMs were reported in the open literature. The most significant advancements made in terms of materials, properties, and testing conditions are described in a chronological fashion.