Copper is one of the most toxic heavy metals which must be eliminated from aqueous environments, according to the environmental standards. Carbohydrate biopolymers are promising candidates for synthesizing copper-adsorbent composites. It is due to unique properties such as having potential adsorptive functional sites, availability, biocompatibility and biodegradability, formability, blending capacity, and reusability. Different types of copper-adsorbent carbohydrate biopolymers like chitosan and cellulose with particular focus on the synthesizing and modification approaches have been tackled in this review. Composites, functionality and morphological aspects of the biopolymer adsorbents have also been surveyed. Further progress in the fabrication and application of biopolymer adsorbents would be achievable with special attention to some critical challenges such as the process economy, copolymer and/or (nano) additive selection, and the physicochemical stability of the biopolymer composites in aqueous media.