This contribution provides an outlook on the topic of furan polymers, dealing with both its main achievements and the salient recent contributions, together with a critical assessment of their most promising perspectives. Following a brief account of the relevant chemical properties of the furan heterocycle, the main monomers from furfural and hydroxymethylfurfural and their respective polymerization mechanisms are discussed. Chain-growth polymerizations concentrate on free-radical and cationic systems, whereas step-growth polymerizations describe the polycondensation of furfuryl alcohol, polyesters, polyamides, polyurethanes and polyureas, poly(Schiff base)s, epoxy resins, and the polycondensation of 5-methylfurfural. Finally, the use of the Diels-Alder reaction applied to furan polymer synthesis and modification is reviewed.