Bio-based polymers have gained high interest the last decades due to the increased concern about diminishing fossil resources and their impact to global warming. According to IUPAC, a biobased polymer is a polymer derived from biomass or issued from monomers derived from biomass and at some stage of its processing into finished products, can be shaped by flow. All these led to the development and growth of a new economy known as bioeconomy. Biobased polymers offer interesting solutions due to their useful functional properties and provide positive impacts on society: low carbon footprint, wider supply base than oil based chemicals, less influenced by fluctuations in oil price, reduction in waste production and landfill use, job positions in rural areas, promoting of the balance between agricultural areas and forests. 2,5-furandicarboxylic acid (2,5-FDCA) is one of the most important diacids for the production of biobased polyesters as films and bottles for food packaging. During the last decade significant progress has been made towards the synthesis of 2,5-FDCA polyesters with different biobased diols and several problems on the aspects of synthesis and properties have been successfully overcome. These are semicrystalline materials and their structural, chemical and physical properties are under investigation. However, some important problems associated with synthesis of polyesters with high molecular weight have to be solved first in order to make them appropriate for industrial applications, specifically their weak mechanical properties and coloration. To this direction, high purity monomers, stabilizers and new catalysts are under investigation by the research community and industries with promising results.