Fluorinated polymers of interest have aromatic groups in their repeat units and at least about 25% of available aromatic ring positions fluorinated. The aromatic rings can be along the polymer backbone and/or along the side chains of the polymer. In particular, for polymers with the aromatic groups along the polymer backbone generally at least about 55 percent of the aromatic ring positions are fluorinated. Approaches for the fluorination of aromatic polymers can involve a polymer melt that is contacted with an appropriate fluorination reagent. In other approaches, the fluorination is performed in a polymer solution. The fluorination reactions can be performed in a batch operation or a continuous operation.