Inorganic acids are commonly used in mining, metallurgical, metal-processing, and nuclear-fuel-reprocessing industries in various processes, such as leaching, etching, electroplating, and metal-refining. Large amounts of spent acidic liquids containing toxic metal ion complexes are produced during these operations, which pose a serious hazard to the living and non-living environment. Developing economic and eco-friendly regeneration approaches to recover acid and valuable metals from these industrial effluents has focused the interest of the research community. Diffusion dialysis (DD) using anion exchange membranes (AEMs) driven by an activity gradient is considered an effective technology with a low energy consumption and little environmental contamination. In addition, the properties of AEMs have an important effect on the DD process. Hence, this paper gives a critical review of the properties of AEMs, including their acid permeability, membrane stability, and acid selectivity during the DD process for acid recovery. Furthermore, the DD processes using AEMs integrated with various technologies, such as pressure, an electric field, or continuous operation are discussed to enhance its potential for industrial applications. Finally, some directions are provided for the further development of AEMs in DD for acid recovery from acidic waste solutions.