Recent studies on anion exchange membranes and electrodialysis methods to permeate specific anions through the membranes are reviewed. The studies are classified: (1) to increase cross-linkage of the anion exchange membranes, (2) to form tight surface layers on the anion exchange membranes, (3) to decrease hydrophilicity of the anion exchange membranes or their surfaces by introducing specific anion exchange groups in the membranes, (4) to impregnate hydrophilic compounds in the anion exchange membranes to increase hydrophilicity of the membranes, (5) to control permselectivity of anions by photoirradiation using membranes with a photoresponsive group and (6) to control permselectivity of anions through thermally responsive anion exchange membranes with temperature. Permselectivity of specific anions through the anion exchange membranes is governed mainly by the balance of hydration energy of anions with hydrophilicity of the membranes, partially by hydrated ionic size of the anions, except the membranes having an oppositely charged layer on the membrane surface.