Adsorption is an important phenomenon widely used for the removal of contaminants. Several drinking water contaminants such as arsenic and fluoride, vanadium and chromium, nickel, cadmium and cobalt are found to coexist in nature as multi-component mixtures in water. Hence, the modeling of multi-component adsorption isotherms for designing water treatment systems has gained importance recently. However, review studies of multi-component adsorption and competitive adsorption modeling are limited. The current review paper summarizes twenty-six multi-component adsorption isotherm models. Also, case studies of several common multi-component adsorption systems and the mechanisms of multi-component adsorption are discussed. Furthermore, a modeling analysis of four multi-component isotherms models for three commonly found two-component adsorption systems, i.e., cadmium-nickel, nickel–cobalt, and cadmium-cobalt, is reported. The Extended Langmuir isotherm, Competitive Langmuir isotherm, Extended Langmuir–Freundlich isotherm and Extended Freundlich isotherm models were applied in the modeling study for the competitive adsorption of Cd, Ni, and Co. The goodness of fit parameters and adsorption isotherm constants were estimated for these models. The factors influencing competitive adsorption, mechanisms of adsorption, various single and multi-component isotherm models, their significance, and limitations are also discussed in this review article.Highlights• Twenty-six multi-component and ten single-component isotherm models are compiled• Factors affecting multi-component competitive adsorption isotherms are discussed in this review paper• The applications of four multi-component isotherm models for three binary contaminant systems are presented.Graphical