In terms of activation mechanism, transition metal compounds react with PS to produce a large amount of ·SO₄⁻; the reaction equation follows:

As can be seen from the above reaction, metal ions are in a free state dispersed in the solution during the reaction process. Although the wastewater can be degraded by the activation persulfate mechanism, it belongs to homogeneous catalysis; metal ions will be dissolved in the aqueous solution, which causes difficult separation from solution. Therefore, the production cost is greatly increased due to its difficult recycling nature, and it is easy to cause secondary pollution to the environment. Therefore, MeFe₂O₄ with a low metal leaching rate has become a new research direction. Through PS/PMS [36] heterogeneous catalytic technology, these problems can be effectively solved [22,37,38].

At present, there are several common methods for preparing iron-based catalysts: hydrothermal, solvothermal, sol–gel preparation, and coprecipitation methods.

In the hydrothermal method, the solute is dispersed into the solution, stirred, and heated in the reactor, and finally washed and dried to obtain the required product [39].

Similar to the hydrothermal method, the solvothermal method changes water into an organic solvent. By dissolving one or more precursors in a nonaqueous solvent, the reaction occurs in liquid phase or supercritical conditions [40].

The sol–gel method is to dissolve the metal alkoxides in organic solvents, form homogeneous solutions, add other components, react at a certain temperature to form gels, and finally make products by drying [41].

Coprecipitation is an important method to prepare composite oxide ultrafine powder containing a large variety of metal elements [42].

The electron transfer between transition metal oxides is much higher [43] than that between single transition metal oxides. Generally, AB₂O₄ [44,45] structure is referred to as spinel structure. CuFe₂O₄ is a typical spinel ferrite with a magnetic structure, which has high chemical stability and low metal leaching rate. Taking CuFe₂O₄ as an example, compared with single transition metal oxides, Fe and Cu elements can play a role in the reaction; respectively, they can also activate PS to produce ·OH and ·SO₄⁻.

G. Xian et al. [46] comprehensively compared the catalytic degradation effects of CoFe₂O₄, CuFe₂O₄, MnFe₂O₄, and ZnFe₂O₄. In detail, CuFe₂O₄ presented the best and fastest catalytic performance in organics removal. Almost 87.6% azo dye acid orange 7 (AO7) was removed in PS solution coupled with CuFe₂O₄ [46]. Additionally, it was known that CuFe₂O₄ had the best catalytic effect. Moreover, through the quenching experiment, it was not ·OH but ·SO₄⁻ that played a major role in the reaction.

Table 1 shows the degradation effects of some different MeFe₂O₄-activated PS/PMS on different kinds of wastewater. It can be seen from the table that the iron-based catalyst with spinel structure mainly acts on ·SO₄⁻ in the mechanism of activation persulfate; the effect of ·OH is slightly worse [47]. Of course, there are also some nonfree radical pathways, which degrade pollutants in water by generating singlet oxygen ¹O₂ [48,49,50].

The carrier recombination method can increase the specific surface area and increase the contact of chemical sites [54], thus greatly improving the rate of chemical reaction. At present, SiO₂ [54,55], black phosphorus [56,57], and rGO [58,59] (reduced graphene oxide) are commonly used as carriers. After compositing with the carrier, it is closely combined with the carrier by van der Waals force [58] or electrostatic interaction [60], making it difficult to fall off the surface of the carrier.

Pure graphene is a benzene-ring-like two-dimensional nanomaterial consisting of sp² hybrid orbitals. However, its high production cost limits its large-scale application. Afterward, by improving Hummer’s method, a large number of oxygen-containing functional groups were linked at the edge of the plane by a strong oxidant, hence the name GO (graphene oxide) (Figure 1); rGO (Figure 2) was obtained by sodium borohydride and other means of reduction, which has low synthesis cost and is suitable for use as a good carrier of catalysis.

Taking CuFe₂O₄, a representative of MeFe₂O₄, as an example, by comparing the effect of pure CuFe₂O₄ with that of CuFe₂O₄ combined with the carrier, it can be seen that the latter has a stronger catalytic effect under acidic and photoinduced conditions [61]. CuFe₂O₄ in CuFe₂O₄–rGO is closely combined with the oxygen-containing groups on rGO through electrostatic interaction, as shown in Figure 3. Images from a scanning electron microscope are shown in Figure 4.

Table 2 shows the degradation effects of some CuFe₂O₄ and rGO composite materials on different kinds of wastewater. It can be seen from the table that the composite catalyst can still produce good effects even without the presence of PS. Not only the Cu, Fe, and other elements in the catalyst can produce pure chemical catalytic effect, but the carrier rGO can produce electron transition under the light condition, promoting the transfer of electrons, and plays a part of the photocatalytic effect [62,63]. Table 2 contains some other carriers, which can also greatly influence degradation of different kinds of wastewater.

In recent years, activation persulfate based on Fe⁰ (zero-valent iron, ZVI) have been widely used in chemical production and environmental remediation [71,72]. As mentioned above, the activation persulfate/Fe (II) mechanism can cause secondary pollution to water, so ZVI/PS [73,74] is used instead to reduce a series of problems caused by the reduction of Fe²⁺ content due to the change of pH and other factors in water [71].

ZVI/PS system has strong reducibility (Fe⁰,E⁰ = −0.44 V) [75]. Compared with CuFe₂O₄, its reaction process is more complex, as shown in Figure 5. Fe⁰ is first converted to Fe²⁺ in the presence of acid and oxidant, then further oxidized to Fe³⁺ by Fe²⁺, and finally to Fe(IV) [76,77]. The reaction mechanism follows [78]: According to the reaction equation, the reaction is easily affected by pH, and the reaction will gradually slow with the increase of pH. Weng et al. [79] point out that the Fe⁰/PS system exhibits two-stage kinetics. The kinetic first stage is mostly attributed to a heterogeneous reaction occurring on the surface of the Fe⁰ aggregate. As the reaction proceeds, decolorization shifts from the slow kinetic first stage to the fast kinetic second stage when sufficient Fe²⁺ ions are maintained in the system [80].

Figure 6 shows the proposed degradation pathway of 2,4-D [82]. By examining Figure 6, it can further confirm that macromolecular organic matter is decomposed into small molecular organic matter, which is gradually mineralized.

Table 3 shows the degradation effects of various types of polluted water bodies activated by PS/PMS based on elemental iron. Usually, an appropriate amount of H₂O₂ [83] will be added to the water when PS is activated by Fe⁰, so as to reduce the cost of oxidant. Through the analysis of the table, it can be seen that the effect of ZVI when used alone [84] is worse than when it is combined with the carrier or when other conditions exist.

Fe₃O₄ magnetite, also known as magnetic iron oxide, is a black crystal with a rotating spinel structure (Figure 7). In magnetite, Fe²⁺ and Fe³⁺ are disordered on the ferrite octahedron, so electrons can transfer rapidly between Fe²⁺ and Fe³⁺; thus, reversible redox reactions can occur at the same position on the octahedron.

However, since Fe₃O₄ is easy to accumulate in solution and contact sites are reduced after agglomeration, single Fe₃O₄ is rarely used. Using the composite carrier method [93] can not only solve these problems, but also speeds the reaction rate, making it more cost effective when applied in industrial production. He et al. [94] pointed out that the Fe₃O₄/GO/Ag composite microspheres are formed using magnetic Fe₃O₄ as cores, followed by coating an internal layer of GO and an outer layer of Ag nanoparticles, as Figure 8 shows. The synthesized Fe₃O₄/GO/Ag composite catalyst under the action of NaBH₄, methylene blue, and ciprofloxacin can be completely degraded within 12 min. Figure 8 shows SEM images of Fe₃O₄/GO/Ag composite catalyst. In Figure 9, we can clearly observe that Ag has been completely attached to the Fe₃O₄/GO surface, which can increase the specific surface area and improve the chemical reaction rate.

Table 4 shows the research progress of Fe₃O₄ and its composite materials on the degradation of different pollutants reported at present. According to the data in the table, when Fe₃O₄ is compounded with the carrier, the catalytic performance is greatly improved.