•Heterogeneous sulfate radical-based advanced oxidation processes were introduced.•Strategies of SFs and SFCs catalyst for PMS activation were overviewed.•Research gaps and needs related to this system were proposed. In recent ten years, the sulfate radical-based advanced oxidation processes (AOPs) have been paid increasing attention due to their superior performance and adaptability in decomposition of organic pollutants. The spinel ferrites (SFs) and spinel ferrite-based composites (SFCs) coupling with peroxymonosulfate (PMS) for heterogeneous catalysis is an efficient way to decompose the organic pollutants by generating reactive sulfate radicals. This article reviewed the recent progress on diverse heterogeneous ferrites (Ni/Cu/Zn/Co/Mn-ferrites) and ferrite composites catalysts (i.e., (Ni/Cu/Zn/Co/Mn-ferrites supported by various substrates) for PMS activation. Besides, impacting factors, synergistic methods of SFs/SFCs-PMS systems in organic decomposition and potential applications were also considered and discussed. Eventually, we proposed the future recommendations and challenges related to SFs and SFCs catalysts, heterogeneous SFs/SFCs-PMS systems and their possible applications in wastewater purification.