Fluorinated block copolymers combine the unique properties of fluoropolymers and the intriguing self-assembly of hybrid macromolecules. The preparation of the title molecules by selective fluorination procedures and the effect of fluorine incorporation on the material thermodynamics are presented. We highlight two fluorination schemes developed in our laboratory, difluorocarbene and perfluoroalkyliodide additions to polydienes, that allow for the selective and tunable incorporation of different fluorinated groups into model block copolymers. The fluorination changes the physical properties of the parent materials and leads to interesting changes in the component incompatibilities. The role of fluorination in determining block copolymer thermodynamics in both the solid state and in solution and in ultimately exploiting fluorination to produce novel, higher order structures is central to our research efforts.