As materials engineered to interact with biological systems for medical purposes, polymeric biomedical materials have revolutionized and are indispensable in modern healthcare. However, aging populations and improving healthcare standards worldwide have resulted in ever-increasing demands for such biomaterials. Currently, many clinically used polymers are derived from nonrenewable petroleum resources, thus spurring the need for exploring alternatives for the next generation of sustainable biomaterials. Other than biomass, this Perspective also spotlights carbon dioxide and postuse plastics as viable resources potentially suitable for biomaterial production. For each alternative feedstock, key recent developments and practical considerations are discussed, including emerging biomaterial applications, possible feedstock sources, and hindrances toward translation and practical adoption. Other than replacements for petroleum-derived polymers, we explore how utilization of these alternatives capitalizes on their intrinsic physiochemical and material properties to achieve their desired therapeutic effects. We hope that this Perspective can stimulate further development in sustainable biomaterials to achieve practical therapeutic benefits as part of a circular materials economy with minimal environmental impact.