The key role of trivalent manganese (Mn(III)) species in promoting sulfate radical-based advanced oxidation processes (SR-AOPs) has recently attracted increasing attention. This review provides a comprehensive summary of Mn(III) (oxyhydr)oxide-based catalysts used to activate peroxymonosulfate (PMS) and peroxydisulfate (PDS) in water. The crystal structures of different Mn(III) (oxyhydr)oxides (such as α-Mn2O3, γ-MnOOH, and Mn3O4) are first introduced. Then the impact of the catalyst structure and composition on the activation mechanisms are discussed, as well as the effects of solution pH and inorganic ions. In the Mn(III) (oxyhydr)oxide activated SR-AOPs systems, the activation mechanisms of PMS and PDS are different. For example, both radical (such as sulfate and hydroxyl radical) and non-radical (singlet oxygen) were generated by Mn(III) (oxyhydr)oxide activated PMS. In comparison, the activation of PDS by α-Mn2O3 and γ-MnOOH preferred to form the singlet oxygen and catalyst surface activated complex to remove the organic pollutants. Finally, research gaps are discussed to suggest future directions in context of applying radical-based advanced oxidation in wastewater treatment processes.