Transport and stability issues of proton and hydroxide ion conducting separator membranes for fuel cells are critically discussed from a fundamental point of view. Considerations of structure and dynamics on the molecular scale to the device level equally imply polymer-chemical and electrochemical aspects which are closely related for this class of materials. The importance of ion/solvent, residual ion/ion, and solvent/polymer interactions for the formation and mobility of ionic charge carriers and selective ionic transport and even as driving forces for nanoscale ordering is emphasized, and it is shown that, apart from simple electrostatics, specific chemical interactions must be considered. On the basis of this understanding, suggestions are being made for the modification of existing and the development of new membrane types, not only for fuel cells but also for other electrochemical energy conversion and storage devices such as redox-flow and alkaline ion batteries.