The contamination of water resources by heavy metals poses a serious environmental risk, and conventional treatment methods face significant limitations. This review addresses the issue by presenting a critical analysis of the development of sustainable biosorbent and biopolymeric materials for heavy metal adsorption, highlighting advances, challenges, and future perspectives. To this end, a systematic bibliometric analysis of 120 documents was conducted, extracted from the Scopus and Web of Science databases, covering the period from 2003 to 2025. The results indicate exponential growth in scientific interest in biopolymers such as cellulose, chitosan, lignin, and alginate, especially in the form of aerogels, which demonstrate high adsorptive capacity through mechanisms such as complexation, chelation, and ion exchange. The analysis also reveals the main factors influencing process efficiency, such as pH, temperature, and contact time. It is concluded that, although these sustainable materials are highly promising, challenges related to scalability, selectivity in complex effluents, and regenerability still need to be overcome to enable their large-scale industrial application, in line with the principles of the circular economy.