Lignin, tannins, and cashew nut shell liquid are considered the main sources of aromatic-based macromolecules. They represent an abundant alternative feedstock for the elaboration of aromatic chemicals and polymers, with a view to replacing some fossil-based fractions. Located in different tissues of plants, these compounds, with a large diversity and structural complexity, have, to date, been considered as byproducts derived from fractionation-separation industrial processes with low added value. In the last decade, the use of click chemistry as a tool for the synthesis of controlled macromolecular architectures has seen much development in fundamental and applied research for a wide range of applications. It could represent a valid solution to overcome the main limitations encountered in the chemical modification of natural sources of chemicals, with an environmentally friendly approach to create new substrates for the development of innovative polymers and materials. After a brief description of the main aromatic biopolymers, including the main extraction techniques, along with their structure and their properties, this Review describes chemical modifications that have mainly been focused on natural polyphenols, with the aim of introducing clickable groups, and their further use for the synthesis of biobased materials and additives. Special emphasis is given to several as-yet unexplored chemical features that could contribute to further fundamental and applied materials science research.