The polymerisation of furan monomers and the exploitation of some of the chemical peculiarities of the furan heterocycle have generated a wide diversity of macromolecular materials based on renewable resources. We present here recent contributions to this field, including ongoing studies on the synthesis and characterisation of novel furan polyesters and on the application of the Diels–Alder reaction to the preparation of linear and branched thermally reversible polyadducts.