As environmental problems become more and more severe, sulfate radical (SO4 center dot-) based advanced oxidation processes (SR-AOPs) are widely recognized for their high removal efficiency of recalcitrant organic pollutants in water. Metal-organic frameworks (MOFs) have attracted wide attention in SR-AOPs due to their outstanding properties (e.g. large surface area, ultra-high porosity, and diversity of material design, etc). Herein, we present an overview of the development and challenges in the synthesis of different types of MOFs, combination of MOFs with other materials (metal centers, conductors, cellulose, etc.) and the construction of catalysts with special structures (core-shell structures and hollow structures) as well as their applications in SR-AOPs for the degradation of organic pollutants. Several review papers have already mentioned the application of a branch of MOFs or simple composites of MOFs in SR-AOP, whereas the latest progresses on the application of MOFs-based materials to SR-AOPs was described rarely. Besides, the degradation mechanism of MOFs as catalysts has not been systematically discussed. To this end, the mechanisms of MOFs and MOF-based materials as catalysts to activate PMS/PS in different systems are analyzed, including radicals and non-radicals pathways. Meanwhile, considering that the research in this field is still in its infancy, a lot of improvements are still needed to effectively promote and implement this technology. (C) 2020 Elsevier Ltd. All rights reserved.