This review presents different chemical modifications of tannins, an abundant source of aromatic biomolecules, to elaborate biobased polymers. Tannins are, after lignins, the most abundant source of natural aromatic biomolecules and can be an alternative feedstock for the elaboration of chemicals, building blocks to develop polymers and materials. Tannins are present in all vascular and some non-vascular plants. One of their major issues is the versatility according to their botanical origin, extraction and purification processes. During the last few decades, tannins have been exploited and chemically modified for the development of new biobased polymers, thanks to their functionality brought by phenolic and aliphatic hydroxyl groups. After a historical overview, this review summarizes the different classes of tannins. Some generalities concerning the extraction techniques of tannins and the corresponding properties are also described. This review provides in detail the different chemical modifications of tannins which have been previously reported, with corresponding pathways and applications. Finally, the main chemical pathways to obtain polymeric materials are especially presented.