This review concerns the chemical structure and synthesis of perfluorinated sulfocationite membranes, among which Nafion, MF-4SC, Flemion, Aciplex-S, and Dow membranes are the most well-known representatives. Special attention is given to main mechanisms controlling the formation of microstructure and its relationship with transport processes and selectivity levels of membranes. Key approaches to the modification of ion-exchange materials, above all involving the synthesis of hybrid membranes containing nanoparticles of inorganic compounds, are described. It is noted that increases in the conductivity and selectivity levels of hybrid membranes are primarily related to changes in structure of pores and channels and in the distribution of the concentration of carriers in them. Some examples of the practical use of perfluorinated membranes in modern technologies are highlighted.