Disclosed are aliphatic-aromatic biodegradable polyesters obtained from aliphatic dicarboxylic acids comprising azelaic acid, sebacic acid, suberic acid, brassylic acid and their esters; polyfunctional aromatic acids of renewable origin and particularly 2,5-furan dicarboxylic acid, and diols, such as 1,2-ethanediol, 1,2-propanediol, 1,3-propanediol, 1,4-butanediol, 1,5-pentanediol, 1,6-haxanediol, 1,7-heptanediol, 1,8-octanediol, 1,9-nonanediol, 1,10-decanediol, 1,11-undecanediol, 1,12-dodecanediol, 1,13-tridecanediol, 1,4-cyclohexanedimethanol, propylene glycol, neopentyl glycol, 2-methyl-1,3-propanediol, dianhydrosorbitol, dianhydromannitol, dianhydroiditol, cyclohexanediol, cyclohexane-methanediol, aromatic diols such as phenols, and furan diol. Also disclosed are blends of the polyesters with other biodegradable polymers of either natural or synthetic origin. The polyesters have properties and viscosity values that make them suitable, after adjusting their molecular weight, for use in numerous practical applications such as films, injection molded products, extrusion coatings, fibers, foams, thermoformed products, extruded profiles and sheets, extrusion blow molding, injection blow molding, rotomolding, stretch blow molding.