Reports that promote persulfate-based advanced oxidation process (AOP) as a viable alternative to hydrogen peroxide-based processes have been rapidly accumulating in recent water treatment literature. Various strategies to activate peroxide bonds in persulfate precursors have been proposed and the capacity to degrade a wide range of organic pollutants has been demonstrated. Compared to traditional AOPs in which hydroxyl radical serves as the main oxidant, persulfate-based AOPs have been claimed to involve different in situ generated oxidants such as sulfate radical and singlet oxygen as well as nonradical oxidation pathways. However, there exist controversial observations and interpretations around some of these claims, challenging robust scientific progress of this technology toward practical use. This Critical Review comparatively examines the activation mechanisms of peroxymonosulfate and peroxydisulfate and the formation pathways of oxidizing species. Properties of the main oxidizing species are scrutinized and the role of singlet oxygen is debated. In addition, the impacts of water parameters and constituents such as pH, background organic matter, halide, phosphate, and carbonate on persulfate-driven chemistry are discussed. The opportunity for niche applications is also presented, emphasizing the need for parallel efforts to remove currently prevalent knowledge roadblocks.