Magnesium-sulfur (Mg-S) batteries have the advantages of high volumetric energy density, intrinsic safety, and low cost of anode and cathode materials. However, current obstacles that preventing practical applications of Mg-S batteries are reflected in the sluggish reaction kinetics of insulative sulfur cathode, designs of compatible electrolytes, and surface optimization of Mg anode against passivation. Regarding the sulfur cathodes, the inherent low conductivity, high volumetric changes, and polysulfide shuttling always result in depressive capacity and utilization. As known, the Mg$^{2+}$ carriers are coordinated with solvents in the electrolyte and need to be desolvated before or during the Mg$^{2+}$ participating in the electrochemical reactions. The desolvation steps and the cathodic or anodic redox steps are intercoupled at the electrode/electrolyte interface, which can be regarded as cascade reactions of different pathways. In this review, the efforts to deal with the high-energy-barrier processes including Mg$^{2+}$ desolvation, Mg$^{2+}$ migration at the interface and in cathode interior, and sulfur conversions are summarized. Importantly, the possible coupling manners between the above processes are highlighted. Then cascade catalysis strategy for accelerating the desolvation and sulfur conversion kinetics on the premise of superior conductivity is further reviewed along with a variety of characterizations from experiments to theoretical simulations. Finally, future development trends and deep understanding in Mg-S batteries are prospected.