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Advanced oxidation processes (AOPs) based on persulfates such as peroxymonosulfate and peroxydisulfate via heterogeneous catalysts have been a research hotspot due to their outstanding performances in removing emerging organic contaminants (OCs). In this Review, we highlight the recent advances in theoretical simulations for persulfate-based AOPs (PS-AOPs) using density functional theory (DFT), with the emphasis on the catalyst properties and the mechanism of persulfate activation over a variety of heterogeneous catalysts (including nanocarbons, metals, and metal oxides). Moreover, the properties of OCs and their degradation mechanism by diverse reactive oxygen species investigated by theoretical computations are also summarized. The descriptors in computational studies and the related structure–performance relationships are discussed. Finally, the challenges and future research focuses of …