Embodiments of the present disclosure encompass vinyl addition and ROMP polymers having at least one type of repeating unit that encompasses a comprise N+(CH3)3OH− moiety. Other embodiments in accordance with the disclosure include alkali anion-exchange membranes (AAEMs) made from one of such polymers, anion fuel cells (AFCs) that encompass such AAEMs and components of such AFCs, other than the AAEM, that encompass one of such polymers.