Carbon neutrality refers to the state of making net‐zero emissions of carbon dioxide (CO2), which is a key concept in tackling global warming. It can be achieved by offsetting carbon emissions as well as balancing reduced and emitted emissions. Globally, CO2 is emitted mainly from fossil fuel power plants. The use of carbon capture and storage technology, including pre‐, post‐, and oxy‐fuel combustion capture, in power plants can provide a carbon‐neutral strategy that allows for the sustainable use of fossil fuels while potentially reducing CO2 emissions. Oxy‐fuel combustion capture facilitates CO2 capture by simplifying combustion products through the reaction of recirculated flue gas with a high‐purity oxygen. Oxygen transport membranes, which produce pure oxygen by oxygen transport via oxides at high temperatures, have attracted increased interest because they can improve overall efficiency when integrated with oxy‐fuel combustion capture. Dual‐phase membranes with fluorite structure have greater potential for commercialization than perovskite‐based single‐phase membranes, which have poor chemical and mechanical properties. However, despite these advantages, their low oxygen permeability remains a critical issue. This review focuses on progress in the development of dual‐phase membranes and summarizes various approaches that can facilitate bulk diffusion and surface exchange, which affect the oxygen permeability.