Adsorption and ion exchange can be effectively employed for the treatment of metal-contaminated wastewater streams. The use of low-cost materials as sorbents increases the competitive advantage of the process. Natural and modified minerals have been extensively employed for the removal of nickel and zinc from water and wastewater. This work critically reviews existing knowledge and research on the uptake of nickel and zinc by natural and modified zeolite, bentonite and vermiculite. It focuses on the examination of different parameters affecting the process, system kinetics and equilibrium conditions. The process parameters under investigation are the initial metal concentration, ionic strength, solution pH, adsorbent type, grain size and concentration, temperature, agitation speed, presence of competing ions in the solution and type of adsorbate. The system's performance is evaluated with respect to the overall metal removal and the adsorption capacity. Furthermore, research works comparing the process kinetics with existing reaction kinetic and diffusion models are reviewed as well as works examining the performance of isotherm models against the experimental equilibrium data.