Natural polymers have emerged as promising candidates for the sustainable development of materials in areas ranging from food packaging and biomedicine to energy storage and electronics. In tandem, there is a growing interest in the design of advanced materials devised from naturally abundant and renewable feedstocks, in alignment with the principles of Green Chemistry and the 2030 Agenda for Sustainable Development. This review aims to highlight some examples of the research efforts conducted at the Research Team BioPol4fun, Innovation in biopolymer-based Functional Materials and Bioactive Compounds, from the Portuguese Associate Laboratory CICECO–Aveiro Institute of Materials at the University of Aveiro, regarding the exploitation of natural polymers (and derivatives thereof) for the development of distinct sustainable biobased materials. In particular, the focus will be given to the use of polysaccharides (cellulose, chitosan, pullulan, hyaluronic acid, fucoidan, alginate, and agar) and proteins (lysozyme and gelatin) for the assembly of composites, coatings, films, membranes, patches, nanosystems, and microneedles using environmentally friendly strategies, and to address their main domains of application.