Fluorinated electrolytes based on the fluorosulfonimide anion are excellent candidates for use in electrochemical power sources. Electrolytes based on copolymers of tetrafluoroethylene with fluorosulfonimide-functionalized trifluorovinyl ether monomers, and also on lithium fluorosulfonimides functionalized with polyethers, have been of particular interest recently. This lecture will present an overview of recent research at Clemson University on these electrolytes. The presentation will focus especially on ionic conductivity of such electrolytes, in relation to their use in rechargeable lithium ion batteries, and in hydrogen-powered PEM-style fuel cells.