The development of polymeric anion-exchange membranes (AEMs) combining high ion conductivity and long-term stability is a major challenge for materials chemistry. AEMs with regularly distributed fixed cationic groups, based on the formation of microporous polymers containing the V-shape rigid Tröger's base units, are reported for the first time. Despite their simple preparation, which involves only two synthetic steps using commercially available precursors, the polymers provide AEMs with exceptional hydroxide conductivity at relatively low ion-exchange capacity, as well as a high swelling resistance and chemical stability. An unprecedented hydroxide conductivity of 164.4 mS cm(-1) is obtained at a relatively a low ion-exchange capacity of 0.82 mmol g(-1) under optimal operating conditions. The exceptional anion conductivity appears related to the intrinsic microporosity of the charged polymer matrix, which facilitates rapid anion transport.