The circular economy plays an important role in the preparation and recycling of polymers. Research groups in different fields, such as materials science, pharmaceutical and engineering, have focused on building sustainable polymers to minimize the release of toxic products. Recent studies focused on the circular economy have suggested developing new polymeric materials based on renewable and sustainable sources, such as using biomass waste to obtain raw materials to prepare new functional bio-additives. This review presents some of the main characteristics of common polymer additives, such as antioxidants, antistatic agents and plasticizers, and recent research in developing bio-alternatives. Examples of these alternatives include the use of polysaccharides from agro-industrial waste streams that can be used as antioxidants, and chitosan which can be used as an antistatic agent.