The increasing occurrence of algal and cyanobacterial blooms and the related formation of algal organic matter (AOM) is a worldwide issue that endangers the quality of freshwater sources and affects water treatment processes. The associated problems involve the production of toxins or taste and odor compounds, increasing coagulant demand, inhibition of removal of other polluting compounds, and in many cases, AOM acts as a precursor of disinfection by-products. Previous research has shown that for sufficient AOM removal, the conventional drinking water treatment based on coagulation/flocculation must be often accompanied by additional polishing technologies such as adsorption onto activated carbon (AC). This state-of-the-art review is intended to serve as a summary of the most current research on the adsorption of AOM onto AC concerning drinking water treatment. It summarizes emerging trends in this field with an emphasis on the type of AOM compounds removed and on the adsorption mechanisms and influencing factors involved. Additionally, also the principles of competitive adsorption of AOM and other organic pollutants are elaborated. Further, this paper also synthesizes previous knowledge on combining AC adsorption with other treatment techniques for enhanced AOM removal in order to provide a practical resource for researchers, water treatment plant operators and engineers. Finally, research gaps regarding the AOM adsorption onto AC are identified, including, e.g., adsorption of AOM residuals recalcitrant to coagulation/flocculation, suitability of pre-oxidation of AOM prior to the AC adsorption, relationships between the solution properties and AOM adsorption behaviour, or AOM as a cause of competitive adsorption. Also, focus should be laid on continuous flow column experiments using water with multi-component composition, because these would greatly contribute to transferring the theoretical knowledge to practice. Display omitted •The adsorption of AOM, toxins and T&O compounds onto GAC/PAC was reviewed.•The combination of adsorption with other water treatment processes was evaluated.•The properties of AOM, AC and solution as main adsorption factors were analysed.•The adsorption mechanisms and the competitive adsorption of AOM were described.•The application of laboratory results in practice was proposed as a future interest.