Sulfate radical-based advanced oxidation processes (AOPs) have been received increasing attention in recent years due to their high capability and adaptability for the degradation of emerging contaminants. Persulfate (PS, S₂O₈²⁻) and peroxymonosulfate (PMS, HSO₅⁻) can be activated by thermal, alkaline, ultraviolet light, activated carbon, transition metal (such as Fe⁰, Fe²⁺, Cu²⁺, Co²⁺, Ag⁺), ultrasound and hydrogen peroxide to form sulfate radical (SO₄⁻), which is strong oxidant and capable of effectively degrading emerging pollutants. Sulfate radical-based AOPs have a series of advantages in comparison with OH-based methods, for example: higher oxidation potential, higher selectivity and efficiency to oxidize pollutants containing unsaturated bonds or aromatic ring, wider pH range. Therefore, sulfate radicals are capable of removing the emerging contaminants more efficiently. In this review paper, various methods for the activation of PS and PMS were introduced, including, thermal, alkaline, radiation, transition metal ions and metal oxide, carbonaceous-based materials activation and so on; and their possible activation mechanisms were discussed. In addition, the application of activated PS and PMS for the degradation of emerging contaminants and the influencing factors were summarized. Finally, the concluding remarks and perspectives are made for future study on the activation of PS and PMS. This review can provide an overview for the activation and application of PS and PMS for the degradation of emerging contaminants, as well as for the deep understanding of the activation mechanisms of PS and PMS by various methods.