Motivated by a general concern on sustainability and environmental issues, a sparkling search for renewable-based polymers has grown exponentially in recent years. This search definitely spotlighted polyesters derived from 2,5-furandicarboxylic acid, among other polymers, as some of the most promising, especially due to the resemblance of this renewable monomer to the well-known petroleum-based terephthalic acid, as well as for the possibility of preparing innovative materials. The huge number of recent papers and patents about this family of polymers explore aspects such diverse as synthesis with other renewable-based monomers, leading to the preparation of materials with enhanced thermo-mechanical, biodegradability and liquid crystalline properties, among other features. Additional aspects pursued in such studies are innovation in the synthetic approaches or its optimisation; and also the development of applications for everyday-life objects like for example packaging materials, especially bottles, textiles, coating, toners, among many other uses. Despite this intense activity little has been reviewed recently about this unique family of polyesters, or derived polymers, as the only reviews on the subject date-back from the last century. In this perspective, the present appraisal aims at contributing to fulfil this literature gap, covering recent aspects related with challenges of developing polyesters, polyamides, or other polymers from 2,5-furandicarboxylic acid and their precursors. Emphasis is placed on monomer synthesis, polymerisation reactions, catalysts and applications.