Polymers, polymer precursors, and other materials are described, having at least one heterocycle and being useful for fabrication of proton-exchange membranes (PEMs). In representative examples, the heterocycle is a fluorinated imidazole ring. The heterocycle can be chosen to have a low value of pKa, and may be a triazole ring, other nitrogen-containing heterocycle, or derivative thereof. Polymers and composites were prepared having excellent proton conductivity. Applications of these materials include fuel cells and other ion-conducting applications.