Described are methods of making a curable fluoropolymer having repeating units derived from vinylidenfluoride (VDF) and at least one perfluorinated monomer selected from hexafluoropropene (HFP), tetrafluoroethene (TFE), a perfluorovinyl ether (PAVE), a perfluoroallylether (PAAVE) or a combination thereof. The method includes polymerizing the monomers in an aqueous medium in a radical reaction containing one or more reaction initiators, one or more chain transfer agent containing one or more halogens selected from iodine, bromine or a combination thereof and one or more non-fluorinated aliphatic polyhydroxy emulsifiers. The polymerization is carried out without adding a fluorinated emulsifier. Also provided are curable fluoropolymers obtainable by such methods and cured fluoropolymers obtainable by curing the curable fluoropolymers, and their applications.