•Copper removal through bioadsorbents is most attractive and low cost treatment option.•Agricultural, microbial, fungal and forest biomasses as potential bioadsorbents.•The need to switch batch to fixed columns studies for field applications.•The importance of understanding the surface chemistry of novel bioadsorbents.•The requirements of low cost and suitable chemical modifications of novel adsorbents. Copper (Cu2+) containing wastewaters are extensively released from different industries and its excessive entry into food chains results in serious health impairments, carcinogenicity and mutagenesis in various living systems. An array of technologies is in use to remediate Cu2+ from wastewaters. Adsorption is the most attractive option due to the availability of cost effective, sustainable and eco-friendly bioadsorbents. The current review is dedicated to presenting state of the art knowledge on various bioadsorbents and physico-chemical conditions used to remediate Cu2+ from waste streams. The advantages and constraints of various adsorbents were also discussed. The literature revealed the maximum Cu adsorption capacities of various bioadsorbents in the order of algae>agricultural and forest>fungal>bacterial>activated carbon>yeast. However, based on the average Cu adsorption capacity, the arrangement can be: activated carbon>algal>bacterial>agriculture and forest-derived>fungal>yeast biomass. The data of Cu removal using these bioadsorbents were found best fit both Freundlich and Langmuir models. Agriculture and forest derived bioadsorbents have greater potential for Cu removal because of higher uptake, cheaper nature, bulk availability and mono to multilayer adsorption behavior. Higher costs at the biomass transformation stage and decreasing efficiency with desorption cycles are the major constraints to implement this technology.