Display omitted •Activation of SO4− precursor salts by nanomaterials (NMs) was reviewed.•NMs effectively activate peroxymonosulfate (PMS) and persulfate (PS) to SO4−.•NMs exhibit high catalytic activity, large surface area and controllable structure.•Improving SO4− based oxidation necessitates novel design of functional NMs. Sulfate radical anion (SO4−) based advanced oxidation technologies (AOTs) have received a great deal of attention due to their high reactivity with the organic contaminants and high selectivity in complex environmental matrices. Among all SO4− activation techniques, the heterogeneous activation of precursor peroxides such as peroxymonosulfate (PMS) and persulfate (PS) by nanostructured materials has demonstrated to be an effective method to generate SO4−. This paper reviews SO4− chemistry and the nanostructured materials that can effectively activate PMS/PS, namely, transition metal-based nano-catalysts, carbon nanomaterials, and nano-composites. In addition, we also discuss the activation mechanisms of PMS/PS initiated by heterogeneous nanostructured materials, emphasizing their catalytic activity, stability, and reusability for the removal of organic contaminants. This review shows that nanostructured materials have promising potential in environmental remediation based on their excellent catalytic efficiency, large specific surface area, and controllable structure. It also provides perspective on potential future studies on the design of novel nanostructured materials and process development in the field of SO4− based AOTs.