It is evident that in the future, the synthesis of polymeric materials will be limited to renewable sources, and incorporation of fossil-based raw materials will be restricted to those from recycled materials. Therefore, there has been an increase in academic and industrial research focused on obtaining different types of high-quality polymers using environmentally friendly alternatives. Tannins are a natural source of polyphenols that are widely distributed in nature. Due to their structural characteristics, biodegradability, and broad abundance, tannins are strong candidates to replace aromatic polymers derived from fossil sources. This review critically addresses the most relevant and innovative techniques for obtaining polymers from tannins. The objective of this work is to give an overview of the tannin polymerization techniques that are currently used, discuss important chemical modifications that allow subsequent tannin polymerization, and showcase the most interesting and innovative applications of tannins. First, to give the reader a better understanding of the subject, this review begins with a clear classification of the types of tannins and their structural characteristics. Later, a comprehensive study of the tannin-based monomers that have been obtained is provided. Finally, less conventional polymerization techniques are detailed, and an analysis of the perspectives of tannin polymerization in the current context is given.