The release of contaminants of environmental concern including heavy metals and metalloids, and contaminants of emerging concern including organic micropollutants from processing industries, pharmaceuticals, personal care, and anthropogenic sources is a growing threat worldwide due to their toxicity, persistence, and bioaccumulative nature and adversely affect the aquatic environment, crops, animals, fisheries, and human health. There is a big challenge to mitigate inorganic and organic contaminants, which together can be coined as contaminants of environmental and emerging concern (CEECs). The physicochemical properties of several CEECs, reveal that they cannot be easily removed by traditional physicochemical processes and are not economically viable for managing mixed contaminants of low concentrations. As a result, low-cost materials must be designed to provide high CEEC removal efficiency. One of the environmentally viable and energy-efficient approaches is biosorption, which involves using either biomass or biopolymers isolated from plants or animals for decontaminating heavy metals in contaminated environments using inherent biological mechanisms. Among chemical constituents in plant biomass, cellulose, lignin, hemicellulose, proteins, polysaccharides, phenolic compounds, and animal biomass include polysaccharides and other compounds to bind heavy metals covalently and non-covalently. These functional groups include - carboxyl, hydroxyl, carbonyl, amide, amine, sulfhydryl, and other groups. Cation-exchange capacities of these bioadsorbents can be improved by applying the chemical modifications. The relevance of chemical constituents and bioactives in animal, as well as plant-derived biosorbents, is highlighted in this comprehensive review for sequestering and bioremediation of CEECs including as many as ten different heavy metals and metalloids co-contaminated with other organic micropollutants.