A comprehensive literature review has been carried out on the sorption of copper ions onto various biosorbents. Extensive research has been carried out using peat as a sorbent and the sorption capacity of copper on different peats varies by a factor of over fifty. Furthermore, this paper identifies that copper sorption capacities have been reported for over thirty other different biosorbents. The paper reviews the capacities of the various biosorbents for copper and discusses the range of kinetic mechanisms used by different researches to correlate kinetic experimental data. The suitability of the various kinetic models for the sorption of copper from wastewaters onto different biosorbents is discussed. The review identifies several deficiencies in the literature. Many of the studies on equilibrium isotherms only apply one method of analysis. Researchers fail to test experimental equilibrium date using several models and do not determine the best fit model by error analysis or by postulating a sorption mechanism. The same criticism is valid for kinetic studies. The application of more than one kinetic model is extremely rare. Another major problem arises in the characterisation of adsorbent materials, since very little information is provided on surface area, pore size distribution, surface activity, particle size, hardness or attrition rates and influence of pH. These are key factors in developing and designing wastewater treatment systems.